Exhibit 5.1

[Pillsbury Winthrop Shaw Pittman LLP letterhead]

June 24, 2013

Chevron Corporation

6001 Bollinger Canyon Road

San Ramon, CA 94583

Gentlemen and Mesdames:

We are acting as counsel for Chevron Corporation, a Delaware corporation (the “Company”), in connection with the issuance by the Company of $750,000,000 in aggregate principal amount of 0.889% Notes Due 2016, $2,000,000,000 in aggregate principal amount of 1.718% Notes Due 2018, $1,000,000,000 in aggregate principal amount of 2.427% Notes Due 2020, and $2,250,000,000 in aggregate principal amount of 3.191% Notes Due 2023 (the “Securities”) pursuant to the Registration Statement on Form S-3 (Registration No. 333-184777) (the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), on November 6, 2012, and the related base prospectus which forms a part of and is included in the Registration Statement, as supplemented by the Prospectus Supplement dated June 17, 2013 filed with the Commission pursuant to Rule 424(b) under the Act (as so supplemented, the “Prospectus”). The Securities will be issued under the Indenture, dated as of June 15, 1995, as supplemented by the Fourth Supplemental Indenture dated as of June 24, 2013 (as so supplemented, the “Indenture”), each being between the Company and Wells Fargo Bank, National Association, as trustee (the “Trustee”).

We have reviewed and are familiar with such corporate proceedings and other matters as we have deemed necessary for the opinions expressed in this letter. In such review, we have assumed that the Indenture has been duly authorized, executed and delivered by the Trustee, the Securities will be properly authenticated by the manual signature of an authorized representative of the Trustee, and the signatures on all documents examined by us are genuine, which assumptions we have not independently verified.

On the basis of the assumptions and subject to the qualifications and limitations set forth herein, we are of the opinion that (i) the Securities have been duly authorized and, when issued and sold in accordance with the Indenture and as contemplated by the Registration Statement and the Prospectus, will constitute the valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms, except as may be limited by applicable bankruptcy, insolvency, fraudulent conveyance, fraudulent transfer, receivership, conservatorship, arrangement, moratorium and other laws affecting and relating to the rights of the creditors generally, by general equitable principles and by requirements of reasonableness, good faith, fair dealing and materiality.

The opinions set forth in this letter are limited to matters governed by the General Corporation Law of the State of Delaware and the laws of the State of New York, in each case as in effect on the date hereof.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Company’s Current Report on Form 8-K filed by the Company with the Commission on the date hereof and the incorporation thereof in the Registration Statement and to the use of our name under the caption “Legal Opinions” in the Prospectus. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission promulgated thereunder.