Exhibit 5.1

Paul, Weiss, Rifkind, Wharton & Garrison LLP

1285 Avenue of the Americas

New York, New York 10019-6064

212-373-3000

212-757-3990

November 24, 2020

vTv Therapeutics Inc.

3980 Premier Drive, Suite 310

High Point, NC 27265

Ladies and Gentlemen:

We have acted as special counsel to vTv Therapeutics Inc., a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-1 (the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Act”), and the rules and regulations thereunder (the “Rules”).  You have asked us to furnish our opinion as to the legality of the securities being registered under the Registration Statement. The Registration Statement relates to the registration under the Act of up to 5,331,306 shares (the “Shares”) of Class A common stock of the Company, par value $0.01 per share (the “Common Stock”), that may be offered by Lincoln Park Capital Fund LLC, an Illinois limited liability company (“Lincoln Park”).

In connection with the furnishing of this opinion, we have examined originals, or copies certified or otherwise identified to our satisfaction, of the following documents:

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In addition, we have examined (i) such corporate records of the Company that we have considered appropriate, including a copy of the certificate of incorporation, as amended, and by-laws, as amended, of the Company certified by the Company as in effect on the date of this letter, and copies of resolutions of the board of directors of the Company relating to the issuance of the Shares, and (ii) such other certificates, agreements and documents that we deemed relevant and necessary as a basis for the opinions expressed below. We have also relied upon the factual matters contained in the representations and warranties of the Company made in the documents reviewed by us and upon certificates of public officials and the officers of the Company.

In our examination of the documents referred to above, we have assumed, without independent investigation, the genuineness of all signatures, the legal capacity of all individuals who have executed any of the documents reviewed by us, the authenticity of all documents submitted to us as originals, the conformity to the originals of all documents submitted to us as certified, photostatic, reproduced or conformed copies of valid existing agreements or other documents, the authenticity of all such latter documents and that the statements regarding matters of fact in the certificates, records, agreements, instruments and documents that we have examined are accurate and complete.

Based upon the above, and subject to the stated assumptions, exceptions and qualifications, we are of the opinion that the Shares have been duly authorized by all necessary corporate action on the part of the Company and, when issued, delivered and paid for in accordance with the terms of the Purchase Agreement, the Shares will be validly issued, fully paid and non-assessable.

The opinion expressed above is limited to the Delaware General Corporation Law. Our opinion is rendered only with respect to the laws, and the rules, regulations and orders under those laws, that are currently in effect.

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We hereby consent to the use of this opinion as an exhibit to the Registration Statement and to the use of our name under the heading “Legal Matters” contained in the prospectus included in the Registration Statement. In giving this consent, we do not thereby admit that we come within the category of persons whose consent is required by the Act or the Rules.

Very truly yours,

/s/ Paul, Weiss, Rifkind, Wharton & Garrison LLP

PAUL, WEISS, RIFKIND, WHARTON & GARRISON LLP