EXHIBIT 5.1

[Letterhead of White & Case LLP]

June 30, 2017

Hess Corporation

1185 Avenue of the Americas

New York, NY 10036

Re: 13,500,000 Shares of Common Stock reserved for issuance pursuant to the Hess Corporation 2017 Long-Term Incentive Plan

Ladies and Gentlemen:

We have acted as counsel to Hess Corporation, a Delaware corporation (the “Company”), in connection with the registration pursuant to the Registration Statement on Form S-8 (the “Registration Statement”) to be filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), of 13,500,000 shares of its common stock, par value $1.00 per share (the “Common Stock”), reserved for issuance pursuant to the Hess Corporation 2017 Long-Term Incentive Plan (the “Plan”).

We have examined such documents, certificates, records, authorizations and proceedings and have made such investigations as we have deemed necessary or appropriate in order to give the opinion expressed herein. We have relied, to the extent we deem such reliance proper, upon such certificates or comparable documents of officers and representatives of the Company and of public officials and upon statements and information furnished by officers and representatives of the Company with respect to the accuracy of material factual matters contained therein which were not independently established by us. In such examination we have assumed, without independent investigation or verification of any kind, the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to authentic original documents of all documents submitted to us as photostatic or certified copies, and the authenticity of the originals of such copies.

Based on the foregoing, and subject to the qualifications, assumptions and limitations stated herein, it is our opinion that the above-referenced 13,500,000 shares of Common Stock reserved for issuance under the Plan have been duly authorized by the Company, and when issued as provided under the Plan, will be validly issued, fully paid and non-assessable shares of Common Stock of the Company.

We do not express or purport to express any opinions with respect to laws other than the General Corporation Law of the State of Delaware.

The opinions set forth in this letter are effective as of the date hereof. We do not undertake to advise you of any changes in our opinion expressed herein resulting from matters that may arise after the date of this letter or that hereinafter may be brought to our attention. We express no opinions other than as herein expressly set forth, and no opinion may be inferred or implied beyond that expressly stated herein. We hereby consent to the filing of this opinion as an exhibit to the above-referenced Registration Statement. In giving this consent, we do not hereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act and the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ White & Case LLP

WHITE & CASE LLP