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
January 29, 2021		Dubai		Riyadh
		Düsseldorf		San Diego
		Frankfurt		San Francisco
		Hamburg		Seoul
		Hong Kong		Shanghai
		Houston		Silicon Valley
		London		Singapore
		Los Angeles		Tokyo
		Madrid		Washington, D.C.
		Milan

Gritstone Oncology, Inc.

5959 Horton Street, Suite 300

Emeryville, California 94608

Ladies and Gentlemen:

We have acted as special counsel to Gritstone Oncology, Inc., a Delaware corporation (the “Company”), in connection with the resale from time to time by the selling stockholders named in the Prospectus (as defined below) of (i) 9,586,478 shares (the “Common Shares”) of Common Stock, par value $0.0001 per share (the “Common Stock”), and (ii) 27,480,719 shares of Common Stock issuable from time to time upon exercise of pre-funded warrants (the “Warrants”) to purchase shares of Common Stock (the “Warrant Shares,” and collectively with the Common Shares, the “Shares”) held by the selling stockholders. The resale of the Shares is being registered pursuant to a registration statement on Form S-3 under the Securities Act of 1933, as amended (the “Act”), filed with the Securities and Exchange Commission (the “Commission”) on January 29, 2021 (Registration No. 333-252564) (the “Registration Statement”), a base prospectus dated January 29, 2021 included in the Registration Statement at the time it originally became effective (the “Base Prospectus”), and a prospectus supplement dated January 29, 2021 filed with the Commission pursuant to Rule 424(b) under the Act (together with the Base Prospectus, the “Prospectus”). 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 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, (a) the issue and sale of the Common Shares have been duly authorized by all necessary corporate action of the Company, and the Common Shares are validly issued, fully paid and non-assessable, and (b) when the Warrant 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, the issue and sale of the Warrant Shares have been duly authorized by all necessary corporate action of the Company, and upon issuance, delivery and payment therefor in the manner contemplated by the Prospectus and the Warrants, 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 Company’s Current Report on Form 8-K dated January 29, 2021 and to the

January 29, 2021

Page 2

reference to our firm contained 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.