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 April 27, 2016 with respect to the consolidated balance sheets of Cheniere Corpus Christi Holdings, LLC and its subsidiaries as of December 31, 2015 and 2014, 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, 2015, included herein and to the reference to our firm under the heading “Experts” in the prospectus.

/s/ KPMG LLP

Houston, TX

January 5, 2017