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  Proskauer
                                            Rose LLP 1001 Pennsylvania Avenue, NW Suite 600 South Washington, DC 20004-2533

June 29, 2023

VIA EDGAR

Alberto Zapata

Senior Counsel

Division of Investment Management

U.S. Securities and Exchange Commission

100 F Street, N.E.

Washington, D.C. 20549

    Re:
    IDR Core Property Index Fund Ltd

    Proxy Statement (Preliminary) on Schedule 14A

    (File No. 811-23460)

Dear Mr. Zapata:

On behalf of IDR Core Property Index Fund Ltd
(the “Company”), set forth below are the Company’s responses to the oral comments provided by the
staff of the Division of Investment Management (the “Staff”) of the Securities and Exchange Commission
(the “Commission”) to the Company on June 13, 2023, with respect to the Company’s Preliminary
Proxy Statement on Schedule 14A (the “Proxy Statement”) (File No. 811-23460), filed with the Commission
on June 2, 2023. The Staff’s comments are set forth below in italics and are followed by the Company’s responses. Capitalized
terms used below but not otherwise defined herein shall have the meanings ascribed to them in the Proxy Statement. Where revisions to
the Proxy Statement are referenced in the below responses, such revisions are indicated by marked pages from the Proxy Statement
attached as an exhibit hereto.

General

 1. Comment: The Staff notes that
                                            the Company filed a Registration Statement on Form N-2 with the Commission on May 12,
                                            2023 (the “Registration Statement”). The disclosure set forth in the Registration
                                            Statement indicates that the Company intends to change its name from “IDR Core Property
                                            Index Fund Ltd” to “Accordant ODCE Index Fund” as part of the conversion
                                            of the Company from a Maryland corporation to a Delaware statutory trust. Please revise the
                                            Proxy Statement where appropriate to highlight the fact that the Company’s name will
                                            change if stockholders approve the matters referenced in the Proxy Statement.

Response:
The Company has revised the stockholder letter included in the forepart of the Proxy Statement in response to the Staff’s comment.
The Company has also made conforming edits, where appropriate, throughout the remainder of the Proxy Statement.

 2. Comment: It appears that the
                                            implementation of a number of the proposals included in the Proxy Statement are contingent
                                            upon stockholders approving certain of the other proposals being presented at the Meeting,
                                            including the Advisory Agreement Proposal and the Sub-Advisory Agreement Proposal. Please
                                            revise the disclosure where appropriate in the Proxy Statement, including in the Q&A
                                            section, to highlight the contingent nature of such proposals.

Response:
The Company has revised the Q&A section of the Proxy Statement in response to the Staff’s comment. The Company has also made
conforming edits, where appropriate, throughout the remainder of the Proxy Statement.

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 3. Comment: While the Company
                                            included a detailed discussion of board considerations relating to Proposals #1 and #2, it
                                            does not appear that the Company has included a similar discussion of board considerations
                                            with respect to the remaining proposals. Please revise the disclosure pertaining to these
                                            remaining proposals to include a discussion of the board considerations relating to such
                                            proposals.

Response:
The Company has revised the disclosure throughout the Proxy Statement in response to the Staff’s comment.

Stockholder Letter

 4. Comment: Disclosure in the
                                            stockholder letter included in the forepart of the Proxy Statement indicates that certain
                                            of the Proposals being voted on by stockholders at the Meeting will only become effective
                                            upon the earlier of the termination of the Interim Advisory Agreement and the date on which
                                            the Company converts to an interval fund structure. Please revise the foregoing disclosure
                                            to also explain what will happen if the Interim Advisory Agreement were to terminate before
                                            completion of the Company’s conversion to an interval fund structure, addressing when
                                            the Company will be deemed to have adopted a fundamental policy pursuant to Rule 23c-3
                                            under the Investment Company Act of 1940, as amended (the “1940 Act”).

Response:
The Company has revised the above-referenced disclosure in response to the Staff’s comment. In addition, the Company advises the
Staff on a supplemental basis that it would only expect the Interim Advisory Agreement to terminate before the Company has completed
its conversion to an interval fund structure in the event that its Registration Statement has not yet become effective as of such date.
In particular, assuming that stockholders approve all of the Proposals at the Meeting, it would anticipate operating under the New Advisory
Agreement and New Sub-Advisory Agreement upon termination of its Interim Advisory Agreement if it had not yet converted to an interval
fund structure. The Company has also made conforming edits, where appropriate, throughout the remainder of the Proxy Statement.

 5. Comment: The Staff notes that,
                                            according to the Registration Statement, the Company’s 80% investment policy adopted
                                            pursuant to Rule 35d-1 under the 1940 Act is a non-fundamental policy. Please confirm
                                            that the Proxy Statement is seeking to make such 80% investment policy non-fundamental, as
                                            we note that such policy appears to have historically been a fundamental one of the Company’s.

Response:
The Company confirms to the Staff that the 80% Policy Proposal included in the Proxy Statement seeks stockholder approval to modify the
express language of the 80% investment policy adopted by the Company pursuant to Rule 35d-1, and to make such policy non-fundamental.

Q&A

 6. Comment: Please break out the
                                            last sentence to the question, “What will happen if the Advisory Agreement Proposal
                                            is not approved?” into a new paragraph.

Response:
The Company has revised the above-referenced disclosure in response to the Staff’s comment.

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 7. Comment: The disclosure included
                                            in the answer to the question, “Will the New Advisory Agreement increase the investment
                                            advisory fee paid by the Company?” indicates that the aggregate advisory fees payable
                                            by the Company will increase if the Advisory Agreement Proposal, Sub-Advisory Agreement Proposal
                                            and other Proposals are approved. Please advise the Staff whether you expect the Company
                                            to comply with the safe-harbor provisions set forth under Section 15(f) of the
                                            1940 Act in view of the assignment and termination of its prior investment advisory agreement
                                            with IDR resulting from a change of control of IDR. If so, please revise your disclosure,
                                            both here and as appropriate throughout the remainder of the Proxy Statement, to discuss
                                            the specific requirements of Section 15(f) and how the Company intends to comply
                                            with such requirements.

Response:
The Company advises the Staff on a supplemental basis that it does not believe that the spin-out transaction (the “Spin-Out”)
which led to a change of control of IDR, and the termination of its prior investment advisory agreement with the Company, was of a nature
that would normally entail compliance with the safe-harbor provisions applicable under Section 15(f) of the 1940 Act. In particular,
while the restructuring that comprised the Spin-Out constituted a technical change of control over the parent to IDR, no party received
any sale proceeds or similar sale consideration arising from the Spin-Out. In addition, while the aggregate advisory fees and expenses
borne by the Company, and indirectly its stockholders, will be higher under the New Advisory Agreement and New Sub-Advisory Agreement,
the increase in such fees and expenses reflects the increased regulatory and operational burden associated with operating a continuously
publicly-offered interval fund, including with daily NAV calculations and related administrative burdens. Accordingly, the Company does
not intend to operate pursuant to the safe-harbor requirements set forth under Section 15(f). The Company has, however, revised
the above-referenced section of the Proxy Statement, as well as other sections where appropriate, to reflect the basis for the change
in advisory fees and expenses if the Proposals are approved by stockholders.

 8. Comment: Please revise the
                                            disclosure included in the answer to the question, “What are the Fundamental Policy
                                            Proposals about?” to more clearly explain the changes to the Company’s investment
                                            objective referenced in the Investment Objective Proposal.

Response:
The Company has revised the above-referenced disclosure in response to the Staff’s comment.

 9. Comment: Please revise the
                                            disclosure included in the answer to the question “What are the Fundamental Policy
                                            Proposals about?” to confirm that NFI-ODCE Index is presently concentrated in the types
                                            of investments expected to fall within the Company’s concentration policy, if revised
                                            in the manner proposed under the Concentration Policy Proposal. In addition, please describe
                                            what would happen under the Company’s concentration policy in the event the investment
                                            focus of the index shifts, or if the Company were to adopt another index with a different
                                            investment focus.

Response:
The Company has revised the above-referenced disclosure in response to the Staff’s comment.

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Proxy Statement – Vote Required

 10. Comment: Under the heading
                                            “Vote Required” we note that you have included a sentence which states that approval
                                            of the New ELA will require the affirmative vote of “a majority of a 1940 Act Majority.”
                                            Please revise the foregoing sentence to remove the first reference to “majority.”

Response:
The Company has revised the above-referenced disclosure in response to the Staff’s comment.

Proxy Statement – Proposal #1

 11. Comment: Disclosure included
                                            under the heading “Background” in the section of the Proxy Statement discussing
                                            Proposal #1 indicates that the Interim Advisory Agreement will expire on September 14,
                                            2023. Please revise the foregoing disclosure to also note what will happen in the event shareholders
                                            fail to approve the New Advisory Agreement prior to termination of the Interim Advisory Agreement.

Response:
The Company has revised the above-referenced disclosure in response to the Staff’s comment.

 12. Comment:
                                            Disclosure included under the heading “Background” in the section of the Proxy
                                            Statement discussing Proposal #1 indicates that the Company does not anticipate that the
                                            engagement of Accordant Investments pursuant to the New Advisory Agreement will have a material
                                            impact on the Company, as IDR is expected to remain as sub-adviser to the Company subsequent
                                            to the Effective Date. Please revise the foregoing disclosure to explain why the Company
                                            believes there will be no anticipated material impact to stockholders, in view of the fact
                                            that advisory fees will be higher under the New Advisory Agreement.

Response:
The Company has revised the above-referenced disclosure in response to the Staff’s comment. In addition, the Company advises the
Staff on a supplemental basis that the reference to “material impact” was intended to refer to the nature and level of advisory
services provided to the Company, which has now been clarified in the revised disclosure.

 13. Comment: Please revise the
                                            footnote to the “Fees & Expenses” table included in the section of the
                                            Proxy Statement discussing Proposal #1 to clarify the assumptions underlying the 0.50% figure
                                            included under the line item “Other Expenses”, including the length of time any
                                            proposed expense waiver reflecting such amount would remain effective.

Response:
The Company has revised the above-referenced disclosure in response to the Staff’s comment.

 14. Comment: Please revise the
                                            Fees & Expenses table included in the section of the Proxy Statement discussing
                                            Proposal #1 to indicate the expected total annual fund operating expenses as a percentage
                                            of the Company’s net asset value in the event stockholders approve the Advisory Agreement
                                            Proposal.

Response:
The Company has revised the above-referenced disclosure in response to the Staff’s comment.

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 15. Comment: Please confirm that
                                            the disclosure set forth in the section of the Proxy Statement discussing Proposal #1 includes
                                            any disclosures required under Item 22(c)(6) of Schedule 14A regarding material interests
                                            of directors.

Response:
The Company has revised the above-referenced disclosure in response to the Staff’s comment. In addition, the Company confirms that
it does not believe that there are any material interests of any of the Co