Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

The Member

Cheniere Corpus Christi Holdings, LLC:

We consent to the use of our report dated March 7, 2017 with respect to the consolidated balance sheets of Cheniere Corpus Christi Holdings, LLC and its subsidiaries as of December 31, 2016 and 2015, and the related consolidated and combined statements of operations, member’s equity, and cash flows for each of the years in the three-year period ended December 31, 2016, included herein and to the reference to our firm under the heading “Experts” in the prospectus. Our report refers to a change in the presentation of cash flows.

/s/ KPMG LLP

Houston, Texas

March 7, 2017