Center Coast Brookfield Core MLP Fund I SC TO-I Issuer tender offer statement

Exhibit 99(a)

EXHIBIT A

COVER LETTER TO OFFER TO PURCHASE AND LETTER OF TRANSMITTAL

IF YOU DO NOT WANT TO SELL YOUR LIMITED LIABILITY COMPANY UNITS AT THIS TIME, PLEASE DISREGARD THIS NOTICE. THIS IS SOLELY NOTIFICATION OF THE FUND’S TENDER OFFER.

February 28, 2018

Dear Center Coast Brookfield Core MLP Fund I, LLC Member:

We are writing to inform you of important dates relating to a tender offer by Center Coast Brookfield Core MLP Fund I, LLC (the “Fund”).If you are not interested in having the Fund repurchase some or all of your limited liability company units (including fractions thereof) (“Units”) valued as of March 31, 2018, please disregard this notice and take no action.

The tender offer period will begin on February 28, 2018 and will end at 11:59 p.m., Eastern Time, onMarch 28, 2018,at which point the tender offer will expire. The purpose of the tender offer is to provide liquidity to Members of the Fund that hold Units. Units may be presented to the Fund for purchase only by tendering them during one of the Fund’s announced tender offers.

Should you wish to tender all or some of your Units for purchase by the Fund during this tender offer period, please complete and return the enclosed Letter of Transmittal so that it is received by UMB Fund Services, Inc. (“UMBFS”) no later thanMarch 28, 2018. If you do not wish to have all or some of your Units repurchased, simply disregard this notice.NO ACTION IS REQUIRED IF YOU DO NOT WISH TO HAVE ANY OF YOUR UNITS REPURCHASED.

If you would like to tender your Units, you should complete, sign and either (i) mail or otherwise deliver the Letter of Transmittal to Center Coast Brookfield Core MLP Fund I, LLC, c/o UMB Fund Services, Inc. at 235 W. Galena Street, Milwaukee, Wisconsin 53212, Attention: Tender Offer Administrator; or (ii) fax it to UMBFS at (816) 860-3140, Attention: Tender Offer Administrator (if by fax, please deliver an original, executed copy promptly thereafter), so that it isreceived before 11:59 p.m., Eastern Time, on March 28, 2018.

If you have any questions, please refer to the enclosed Offer to Purchase document, which contains additional important information about the tender offer, or call the Tender Offer Administrator at UMBFS at (855) 552-5200.

Sincerely,

Center Coast Brookfield Core MLP Fund I, LLC