Exhibit 5.1

Andrews Kurth Kenyon LLP 600 Travis, Suite 4200 Houston, Texas 77002 +1.713.220.4200 Phone +1.713.220.4285 Fax andrewskurthkenyon.com

November 2, 2017

Cheniere Corpus Christi Holdings, LLC

700 Milam Street, Suite 1900

Houston, Texas 77002

Re: Cheniere Corpus Christi Holding, LLC Registration Statement on Form S-4.

Ladies and Gentlemen:

We have acted as special counsel to Cheniere Corpus Christi Holdings, LLC, a Delaware limited liability company (the “Issuer), in connection with the public offering of $1,500,000,000 aggregate principal amount of the Issuer’s 5.125% Senior Notes due 2027 (the “Exchange Notes”), which are to be guaranteed pursuant to guarantees thereof (the “Guarantees”) by each of the subsidiaries of the Issuer that is listed in Exhibit A hereto (the “Guarantors”). The Issuer and the Guarantors are referred to collectively herein as the “Obligors.”

The Exchange Notes are to be issued under the Indenture (as defined below) pursuant to an exchange offer (the “Exchange Offer”) by the Issuer, in exchange for a like principal amount of the Issuer’s issued and outstanding 5.125% Senior Notes due 2027 (the “Original Notes”), as contemplated by the Registration Rights Agreement (as defined below).

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act of 1933, as amended (the “Securities Act”).

In connection with this opinion, we have examined originals or copies, certified or otherwise identified to our satisfaction, of:

(i) the registration statement on Form S-4 of the Obligors, filed with the Securities and Exchange Commission (the “SEC”) on November 2, 2017 (the “Registration Statement”);

(ii) the Registration Rights Agreement dated as of May 15, 2017 (the “Registration Rights Agreement”) among the Issuer, the subsidiaries of the Issuer party thereto and the initial purchasers party thereto;

(iii) the Indenture dated as of May 18, 2016, among the Issuer, the Guarantors and The Bank of New York Mellon, as trustee (the “Trustee”), as amended and supplemented by the First Supplemental Indenture thereto, dated as of December 9, 2016 and the Second Supplemental Indenture thereto, dated as of May 19, 2017 (such Indenture, as so amended and supplemented being referred to herein as, the “Indenture”); and

ANDREWS KURTH KENYON LLP

Austin  Beijing  Dallas  Dubai  Houston  London  New York  Research Triangle Park  Silicon Valley  The Woodlands  Washington, DC

Cheniere Corpus Christi Holdings, LLC

November 2, 2017

Page 2

(iv) the form of the Exchange Notes attached as an exhibit to the Indenture.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Obligors and such agreements, certificates of public officials, certificates of officers or other representatives of the Obligors and others, and such other documents, certificates and records as we have deemed necessary or appropriate as a basis for the opinions set forth herein. In rendering the opinions set forth below, we have assumed and have not verified (i) the genuineness of the signatures on all documents that we have examined, (ii) the legal capacity of all natural persons, (iii) the authenticity of all documents supplied to us as originals, (iv) the conformity to the authentic originals of all documents supplied to us as certified, photostatic or faxed copies, (v) the authenticity of the originals of such latter documents and (vi) that the Registration Statement, and any amendments thereto (including post-effective amendments), will have become effective and the Exchange Notes will be issued in compliance with applicable federal and state securities laws and in the manner described in the Registration Statement.

In conducting our examination of executed documents, we have assumed (i) the valid existence and good standing of each of the parties thereto (other than the Obligors), (ii) that such parties (other than the Obligors) had the power and authority (corporate, partnership, limited liability company or other) to enter into and to incur and perform all their obligations thereunder, (iii) the due authorization by all requisite action (corporate, partnership, limited liability company or other) by such parties (other than the Obligors) and (iv) the due execution and delivery of such documents by such parties (other than the Obligors).

The opinions expressed herein are limited solely to (i) the laws of the State of New York that are normally applicable to transactions of the type contemplated by the Indenture, the Exchange Notes and the Guarantees, (ii) the laws of the State of Texas, (iii) the Delaware Revised Uniform Limited Partnership Act and (iv) the Delaware Limited Liability Company Act. We express no opinion concerning any other laws.

Based upon and subject to the foregoing and the limitations, qualifications, exceptions and assumptions set forth herein, we are of the opinion that when the Exchange Notes (in the form examined by us) have been duly executed by the Issuer, authenticated by the Trustee in accordance with the terms of the Indenture and issued and delivered upon consummation of the Exchange Offer against receipt of Original Notes surrendered in exchange therefor in accordance with the terms of the Exchange Offer, the Registration Rights Agreement and the Indenture, (i) the Exchange Notes will constitute valid and legally binding obligations of the Issuer and (ii) the Guarantees will constitute valid and legally binding obligations each of the Guarantors.

Our opinions expressed above are subject to applicable bankruptcy, insolvency (including, without limitation, all laws relating to fraudulent transfer or conveyance), reorganization, moratorium and other similar laws affecting creditors’ rights generally and to general principles of equity (regardless of whether enforcement is sought in a proceeding in equity or at law), including, without limitation, (i) the possible unavailability of specific performance, injunctive relief or any other equitable remedy and (ii) concepts of materiality, reasonableness, good faith and fair dealing, and we express no opinion herein with respect to provisions relating to severability or separability.

Cheniere Corpus Christi Holdings, LLC

November 2, 2017

Page 3

We hereby consent to the filing of this opinion with the SEC as an exhibit to the Registration Statement. We also consent to the reference to our firm under the caption “Legal Matters” in the Registration Statement. In giving this consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the SEC. This opinion is expressed as of the date hereof, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in law.

Very truly yours,

/s/ ANDREWS KURTH KENYON LLP

Exhibit A

Guarantors

Name of Guarantor	State or other jurisdiction of incorporation or organization
Corpus Christi Liquefaction, LLC	Delaware
Cheniere Corpus Christi Pipeline, L.P.	Delaware
Corpus Christi Pipeline GP, LLC	Delaware

A-1