Exhibit 5.1

February 25, 2020

Kura Oncology, Inc.

3033 Science Park Road, Suite 220

San Diego, CA  92121

Ladies and Gentlemen:

You have requested our opinion, as counsel to Kura Oncology, Inc., a Delaware corporation (the “Company”), with respect to certain matters in connection with the filing by the Company of a Registration Statement on Form S-8 (the “Registration Statement”) with the Securities and Exchange Commission, covering the offering of up to 1,815,361 shares of the Company's Common Stock, $0.0001 par value (the “Shares”), pursuant to the Company’s Amended and Restated 2014 Equity Incentive Plan (the “Incentive Plan”).

In connection with this opinion, we have examined and relied upon the Registration Statement and related prospectuses, the Incentive Plan, the Company's Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, each as currently in effect, and originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below.  We have assumed the genuineness and authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies thereof, the accuracy, completeness and authenticity of certificates of public officials, and the due authorization, execution and delivery, by all persons other than by the Company, of all documents where due authorization, execution and delivery are a prerequisite to the effectiveness thereof..  As to certain factual matters, we have relied upon a certificate of officers of the Company and have not sought independently to verify such matters.

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware.  We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when issued and sold in accordance with the Incentive Plan, the Registration Statement and related prospectus, will be validly issued, fully paid and nonassessable (except as to shares issued pursuant to certain deferred payment arrangements under the Incentive Plan which will be fully paid and nonassessable when such deferred payments are made in full).

We consent to the filing of this opinion as an exhibit to the Registration Statement.

Sincerely,

Cooley LLP

By:  /s/ Charles J. Bair

     Charles J. Bair

4401 Eastgate Mall, San Diego, CA 92121  T: (858) 550-6000  F: (858) 550-6420  www.cooley.com