Exhibit (a)(1)(i)

BLACKSTONE ALTERNATIVE ALPHA FUND

c/o Blackstone Alternative Asset Management L.P.

345 Park Avenue, 28th Floor

New York, New York 10154

If you do not want to sell your shares of beneficial

interest at this time, please disregard this notice.

This is simply a notification of the Fund’s repurchase offer.

June 20, 2019

Dear Shareholder:

This letter serves to inform you of important dates relating to a repurchase offer by Blackstone Alternative Alpha Fund (the “Fund”). If you are not interested in tendering your shares of beneficial interest in the Fund (“Shares”) for repurchase at this time, please disregard this notice and take no action.

Please note that the sale of Shares that were issued on or after November 1, 2018 will be subject to an “early withdrawal fee,” which will reduce your proceeds by 2%. In addition, the sale of Shares may also be subject to income and transfer taxes.

The tender offer period will begin on June 20, 2019 and end at 11:59 p.m., Eastern Time, on July 22, 2019. The purpose of the tender offer is to provide liquidity to shareholders of the Fund. Shares may be presented to the Fund for repurchase only by tendering them during one of the Fund’s announced tender offers.

If you do not wish to sell your Shares for any reason, simply disregard this notice. No action is required if you do not wish to sell any portion of your Shares at this time.

Should you wish to tender all or some of your Shares during this tender offer period, please complete the enclosed Letter of Transmittal and return it by mail or fax to the Fund’s administrator State Street Bank and Trust Company, Attention: Blackstone Alternative Alpha Fund, 1 Heritage Drive, Mail Code: OHD0100, North Quincy, MA 02171, Fax: (617) 956-0400, or to your financial advisor, as instructed in the Letter of Transmittal.

All Shareholders tendering Shares should carefully review their Letter of Transmittal and follow the delivery instructions therein.

All tenders of Shares must be received in good order by the Fund’s administrator by 11:59 p.m., Eastern Time, on July 22, 2019.

If you have any questions, please refer to the attached Offer to Purchase document, which contains additional important information about the repurchase offer, or call (855) 890-7725.

Sincerely,

Blackstone Alternative Alpha Fund