Contango Oil & Gas (MCF) 8-K Entry into a Material Definitive Agreement

Exhibit 5.1

Gibson, Dunn & Crutcher LLP   811 Main Street Houston, TX 77002-6117 Tel 346.718.6600 www.gibsondunn.com

Client: 21283-00001

November 19, 2018

Contango Oil & Gas Company

717 Texas Ave., Suite 2900

Houston, Texas 77001

Re: Contango Oil & Gas Company

Registration Statement on Form S-3 (File No. 333-215784)

Ladies and Gentlemen:

We have examined the Registration Statement on FormS-3, FileNo. 333-215784 (the “Registration Statement”), of Contango Oil & Gas Company, a Delaware corporation (the “Company”), filed with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), together with the preliminary prospectus thereto filed by the Company pursuant to Rule 424(c) under the Securities Act, in connection with the offering by the Company of up to 8,625,000 shares of the Company’s common stock, par value $0.04 per share (the “Shares”), and associated preferred share purchase rights (the “Rights”), the terms of which are set forth in the Rights Agreement between the Company and Continental Stock Transfer & Trust Company, as rights agent, dated as of August 1, 2018 (the “Rights Agreement”).

In arriving at the opinion expressed below, we have examined originals, or copies certified or otherwise identified to our satisfaction as being true and complete copies of the originals, of such documents, corporate records, certificates of officers of the Company and of public officials and other instruments as we have deemed necessary or advisable to enable us to render the opinions set forth below. In our examination, we have assumed without independent investigation the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies.

Based upon the foregoing, and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that the Shares, when issued against payment therefor as set forth in the Registration Statement, will be validly issued, fully paid andnon-assessable and the Rights will be validly issued.

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November 19, 2018

Page 2

With respect to our opinion concerning the Rights, we express no opinion regarding the Rights Agreement or whether or not the Board of Directors in adopting the Rights Agreement and approving the issuance of the Rights acted in a manner consistent with its fiduciary duties under applicable law and such opinion is based upon the assumption that such adoption and issuance was consistent with such duties. Furthermore, we advise you that the Board of Directors of the Company may be required to redeem or terminate, or take other action with respect to, the Rights at some future time based on the facts and circumstances existing at that time.

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Legal Matters” in the Registration Statement and the prospectus that forms a part thereof. In giving these consents, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations of the Commission.

Very truly yours,

/s/ Gibson, Dunn & Crutcher LLP