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SCHEDULE 14A INFORMATION

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Eaton Vance Senior Income Trust

(Name of Registrant as Specified in Its Charter)

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EATON VANCE SENIOR INCOME TRUST

Two International Place

Boston, Massachusetts 02110

Thomas E. Faust Jr.
President and Chief Executive Officer, Eaton Vance Management
Trustee, Eaton Vance Senior Income Trust

Dear Shareholder:

The annual meeting of shareholders of Eaton Vance Senior Income Trust (the Fund) is scheduled for November 12, 2020. We need your help. An opportunistic hedge fund has acquired a stake in the Fund and has proposed Trustee nominees that your Board believes are not in the best interests of the Fund or its shareholders. Please take the time to vote now. The Board unanimously recommends a vote FOR each of the incumbent Board nominees on the WHITE proxy card. We have not received your vote to this point, and would greatly appreciate your acting on this matter today.

We encourage you to utilize one of the following easy options for voting today:

1. Vote by Telephone. You may cast your vote by telephone by calling the toll-free number listed on the enclosed WHITE proxy card and following the prerecorded information. If you would like to do so with a representative, please call (800) 992-3086.

2. Vote Through the Internet. You may cast your vote using the Internet by logging onto the Internet address located on the enclosed WHITE proxy card and following the instructions on the website.

3. Vote by Mail. You may cast your vote by mail by signing, dating and mailing the enclosed WHITE proxy card in the postage-prepaid return envelope provided.

The Board of Trustees of your Fund recommends that you vote FOR

the election of the Board nominees on the enclosed WHITE proxy card.

If you have any questions regarding anything contained in this letter or would like to receive a copy of the Fund’s proxy statement, please call toll free (800) 992-3086. You may also view the proxy statement online at https://funds.eatonvance.com/closed-end-fund-and-term-trust-documents.php.

Thank you for your attention to this important matter.

Sincerely,

President and Chief Executive Officer, Eaton Vance Management

Trustee, Eaton Vance Senior Income Trust

YOUR VOTE IS IMPORTANT. PLEASE VOTE USING THE WHITE PROXY CARD TODAY.