Exhibit (a)(1)(i)

GOLUB CAPITAL PRIVATE INCOME FUND I

c/o GC Advisors LLC

200 Park Avenue, 25th Floor

New York, New York 10166

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 29, 2026

Dear Shareholder:

This letter serves to inform you of important dates relating to a repurchase offer by Golub Capital Private Income Fund I (the “Fund”). If you are not interested in selling 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, except as described below, all Shares that have been issued after July 1, 2025 will be subject to an “early repurchase deduction” (except in the case of death, divorce or qualified disability of a shareholder; in the event that a shareholder’s shares are repurchased because the shareholder has failed to maintain the $500 minimum account balance; due to trade or operational error; or if repurchase requests are made by certain feeder vehicles), which will reduce your proceeds by 2%. Shares that are issued pursuant to the Fund’s distribution reinvestment plan and tendered will not be subject to the early repurchase deduction. In addition, the sale of Shares may also be subject to income and transfer taxes.

The tender offer period will begin on June 29, 2026 and end at 11:59 p.m., Eastern Time, on July 29, 2026 (the “Expiration Date”). The purpose of the tender offer is to provide liquidity to shareholders of the Fund (“Shareholders”). 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 email to the Fund’s transfer agent, Ultimus Fund Solutions, LLC (the “Transfer Agent”), Attention: Golub Capital Private Income Fund I, using one of the below options or to your financial advisor as instructed in the Letter of Transmittal:

If your shares are held at your financial advisor, broker, dealer or other financial intermediary (“Authorized Intermediary”), please ask your Authorized Intermediary sufficiently in advance of the Expiration Date to submit a repurchase request for you. You may be charged a transaction fee by your Authorized Intermediary for this service. Note that certain Shareholders may be required to deliver their Letter of Transmittal to their Authorized Intermediary for the repurchase request to be considered in good order. However, such Shareholders should submit their Letter of Transmittal to the Fund at the same time they submit the Letter of Transmittal to their Authorized Intermediary. Additionally, for accounts held through a custodial relationship, Shareholders should send the completed Letter of Transmittal to such custodian (along with any custodian required documentation) at the same time the Letter of Transmittal is submitted to the Fund. 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 Transfer Agent by 11:59 p.m., Eastern Time, on July 29, 2026.

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 (833) 327-4024.

Sincerely,

Golub Capital Private Income Fund I