Exhibit 5.1

		140 Scott Drive
		Menlo Park, California 94025
		Tel: +1.650.328.4600  Fax: +1.650.463.2600
		www.lw.com
		FIRM / AFFILIATE OFFICES
		Beijing		Moscow
		Boston		Munich
		Brussels		New York
		Century City		Orange County
		Chicago		Paris
September 17, 2018		Dubai		Riyadh
		Düsseldorf		Rome
		Frankfurt		San Diego
		Hamburg		San Francisco
		Hong Kong		Seoul
		Houston		Shanghai
		London		Silicon Valley
		Los Angeles		Singapore
		Madrid		Tokyo
		Milan		Washington, D.C.

Gritstone Oncology, Inc.

5858 Horton Street, Suite 210

Emeryville, CA 94608

Ladies and Gentlemen:

We have acted as special counsel to Gritstone Oncology, Inc., a Delaware corporation (the “Company”), in connection with the proposed issuance of up to 6,982,142 shares of common stock, $0.0001 par value per share (the “Shares”). The Shares are included in a registration statement on Form S-1 under the Securities Act of 1933, as amended (the “Act”), filed with the Securities and Exchange Commission (the “Commission”) on August 23, 2018 (Registration No. 333-226976) (as amended, the “Registration Statement”). This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or related prospectus (the “Prospectus”), other than as expressly stated herein with respect to the issue of the Shares.

As such counsel, we have examined such matters of fact and questions of law as we have considered appropriate for purposes of this letter. With your consent, we have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters. We are opining herein as to the General Corporation Law of the State of Delaware (the “DGCL”), and we express no opinion with respect to any other laws.

Subject to the foregoing and the other matters set forth herein, it is our opinion that, as of the date hereof, when the Shares shall have been duly registered on the books of the transfer agent and registrar therefor in the name or on behalf of the purchasers and have been issued by

September 17, 2018

Page 2

the Company against payment therefor in the circumstances contemplated by the form of underwriting agreement most recently filed as an exhibit to the Registration Statement, the issue and sale of the Shares will have been duly authorized by all necessary corporate action of the Company, and the Shares will be validly issued, fully paid and nonassessable. In rendering the foregoing opinion, we have assumed that the Company will comply with all applicable notice requirements regarding uncertificated shares provided in the DGCL.

This opinion is for your benefit in connection with the Registration Statement and may be relied upon by you and by persons entitled to rely upon it pursuant to the applicable provisions of the Act. We consent to your filing this opinion as an exhibit to the Registration Statement and to the reference to our firm in the Prospectus under the heading “Legal Matters.” In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.