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1(213) 683-6188

jonathanko@paulhastings.com

August 5, 2024

VIA EDGAR

U.S. Securities and Exchange Commission

Division of Corporation Finance

Office of Real Estate & Construction

100 F Street, NE

Washington, D.C. 20549

 Attention: Pearlyne Paulemon

Pam Howell

Frank Knapp

Jennifer Monick

 Re: Vine Hill Capital Investment Corp.

Registration Statement on Form S-1

Filed July 18, 2024

File No. 333-280880

Ladies and Gentlemen:

On behalf of Vine Hill Capital
Investment Corp., a Cayman Islands exempted company (the “Company,” “we,” “us,”
or “our”), reference is made to the letter dated July 31, 2024 (the “Comment Letter”)
from the staff (the “Staff”) of the Division of Corporation Finance of the Securities and Exchange Commission
(the “Commission”) regarding the above-referenced Registration Statement on Form S-1, filed with the Commission
on July 18, 2024 (the “Registration Statement”).

Separately today, the Company
has filed with the Commission Amendment No. 1 to the Registration Statement (“Amendment No. 1”) through EDGAR
in response to the Staff’s comments.

For your convenience, each
of the Staff’s comments contained in the Comment Letter is duplicated below in bold and is followed by our responses thereto (including
page references to Amendment No. 1, when applicable). Capitalized terms used but not otherwise defined herein have the meanings ascribed
to such terms in Amendment No. 1.

Registration Statement on Form S-1 submitted July 18, 2024

Summary, page 1

 1. We refer you to your tabular presentation of dilution at quartile intervals on the outside cover page
and on pages 40 and 41. Such tabular presentation appears to assume your maximum redemption threshold is the entire amount of shares to
be sold to public shareholders as part of this offering. We further note your disclosure throughout your filing that you may not redeem
your public shares in an amount that would cause your net tangible assets, after payment of the deferred underwriting commissions, to
be less than $5,000,001. Please tell us how you considered this redemption restriction in your determination of your maximum redemption
threshold for your dilution presentation. Please refer to Item 1602 of Regulation S-K.

In response to the
Staff’s comment, we have revised the maximum redemption scenario as well as the other redemption scenarios in the dilution presentation
on the outside cover page and pages 40 and 41 to account for the redemption limitation requiring net tangible assets of at least $5,000,001.
We have also added disclosure to clarify that the dilution presentation takes into account such redemption limitation.

Securities and Exchange Commission

August 5, 2024

Page 2

Competitive Strengths,
page 3

 2. We note the revisions made in response to prior comment 8. Please revise the disclosure beginning on
page 5 to include disclosure regarding NewHold Investment Corp II.

We supplementally
advise the Staff that our special advisor is the only individual who was affiliated with NewHold Investment Corp. II and is not a member
of our management team, which is defined as our directors and officers. In response to the Staff’s comment, we have revised Amendment
No. 1 on pages 5 and 6 to include disclosure regarding our special advisor’s involvement with NewHold Investment Corp. II.

Our Sponsor, page 11

 3. We partially reissue prior comment 13. Please revise the table disclosing the nature and amount of
compensation received or to be received to include the anti-dilution adjustment of the founder shares. See Items 1602(b)(6) of Regulation
S-K.

In response to the
Staff’s comment, we have revised the table on page 12 of Amendment No. 1.

 4. We note your response to prior comment 14. Please clarify the exception to transfer restrictions by
virtue of the sponsor's LLC agreement. See Item 1603(a)(6) of Regulation S-K.

In response to the
Staff’s comment, we have revised the table on page 13 of Amendment No. 1.

Risk Factors, page 39

 5. We partially reissue prior comment 18. We note your disclosure beginning on page 68 that the assets
in your trust account will be securities, including U.S. Government securities or shares of money market funds registered under the Investment
Company Act and regulated pursuant to rule 2a-7 of that Act. Please revise to include disclosure with respect to the consequences to investors
if you are required to wind down your operations as a result of this status, such as any warrants, which would expire worthless.

In response to the
Staff’s comment, we have revised Amendment No. 1 on page 69.

*         *         *         *

Securities and Exchange Commission

August 5, 2024

Page 3

If you have any questions
or require additional information in the course of your review of the foregoing, please call me at (213) 683-6188.

Thank you for your time and
attention.

    Very truly yours,

    /s/ Jonathan Ko

    Jonathan Ko

    of PAUL HASTINGS LLP

 cc: Nicholas Petruska, Vine Hill Capital Investment Corp.

Daniel Zlotnitsky, Vine Hill Capital Investment Corp.

Stuart Neuhauser, Ellenoff Grossman & Schole LLP