G1 Therapeutics (GTHX) 8-K G1 Therapeutics Announces Pricing of Offering of Common Stock

Exhibit 5.1

One Financial Center Boston, MA 02111 617-542-6000 617-542-2241 fax www.mintz.com

September 19, 2018

G1 Therapeutics, Inc.

79 T.W. Alexander Drive

4501 Research Commons, Suite 100    

Research Triangle Park, NC 27709

Ladies and Gentlemen:

This opinion is furnished to you in connection with a Prospectus Supplement, dated September 19, 2018, to a Prospectus dated June 15, 2018 (the “Prospectus and Prospectus Supplement”), filed pursuant to an automatic shelf registration statement on FormS-3ASR, RegistrationNo. 333-225678 (the “Registration Statement”), filed by G1 Therapeutics, Inc., a Delaware corporation (the “Company”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), with respect to an aggregate of 3,450,000 shares (the “Shares”) of its common stock, $0.0001 par value per share (the “Common Stock”), which includes 450,000 shares of Common Stock that may be sold pursuant to the exercise of an option to purchase additional shares. The Shares are to be sold pursuant to an Underwriting Agreement (the “Underwriting Agreement”) dated September 18, 2018 by and among the Company and J.P. Morgan Securities, LLC and Cowen and Company, LLC, as representatives of the underwriters listed in Schedule 1 thereto, which will be filed as an exhibit to a Current Report on Form8-K and incorporated by reference into the Registration Statement.

In connection with this opinion, we have examined the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, each as currently in effect; the minutes of all pertinent meetings of directors of the Company relating to the Registration Statement, the Prospectus and Prospectus Supplement and the transactions contemplated thereby; such other records of the corporate proceedings of the Company and certificates of the Company’s officers as we have deemed relevant for the purposes of rendering the opinions in this letter; the Registration Statement and the exhibits thereto filed with the Commission; and the Prospectus and Prospectus Supplement.

In our examination, we have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, photostatic or facsimile copies and the authenticity of the originals of such copies.

Our opinion is limited to the General Corporation Law of the State of Delaware and we do not express any opinion as to the laws of any other jurisdiction other than the United States Federal Laws and the reported judicial decisions interpreting those laws. To the extent that any applicable document is stated to be governed by the laws of another jurisdiction, we have assumed for

G1 Therapeutics, Inc.

September 19, 2018

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purposes of this opinion that the laws of such jurisdiction are identical to the state laws of the State of Delaware. No opinion is expressed herein with respect to the qualification of the Shares under the securities or blue sky laws of any state or any foreign jurisdiction.

Based upon the foregoing, and subject to the limitations set forth below, we are of the opinion that the Shares, when issued by the Company and delivered by the Company against payment therefor as contemplated by the Underwriting Agreement, will be duly and validly issued, fully paid andnon-assessable shares of the Common Stock.

Please note that we are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matters. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions, and we disclaim any obligation to advise you of any change in any of these sources of law or subsequent legal or factual developments which might affect any matters or opinions set forth herein.

We hereby consent to the filing of this opinion with the Commission as an exhibit to a Current Report on Form8-K and the Registration Statement in accordance with the requirements of Item 601(b)(5) of RegulationS-K under the Securities Act and to the use of this Firm’s name therein and in the Prospectus and Prospectus Supplement under the caption “Legal matters.” In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

Very truly yours,

  /s/ Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C.

MINTZ, LEVIN, COHN, FERRIS, GLOVSKY

    AND POPEO, P.C.