Exhibit 99.1

TEL OFFSHORE TRUST

THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A., CORPORATE TRUSTEE

919 CONGRESS AVENUE / AUSTIN, TEXAS 78701 / (512) 236-6599

TEL OFFSHORE TRUST ANNOUNCES SALE OF ROYALTY INTEREST

AUSTIN, TEXAS JUNE 27, 2016—TEL OFFSHORE TRUST (the “Trust”) announced that the TEL Offshore Trust Partnership (the “Partnership”) has consummated a sale of the Partnership’s remaining overriding royalty interest in certain oil and gas properties located offshore Louisiana (the “Royalty Properties”).  As previously disclosed, on July 10, 2014, the trustees of the Trust (the “Trustees”) filed a Petition for Modification and Termination of the Trust (the “Petition”) with the Probate Court of Travis County, Texas (the “Court”). The Petition requested that the Court modify the Trust’s Trust Agreement to (1) allow for the termination of the Trust by a court order, and (2) allow the Trustees, as necessary to fulfill the purposes of the Trust and without unit holder approval to (a) sell all or any portion of the Trust’s interests in the Partnership or any other assets of the Trust, (b) exercise their rights to dissolve the Partnership, or (c) cause the Partnership to sell the Partnership’s remaining overriding royalty interest.  On June 24, 2016, the Partnership consummated the sale of all of the remaining 60% overriding royalty interest (or 15% of 8/8ths) owned by the Partnership.  The sale was made in accordance with that certain Final Judgment and Order entered by the Court on January 15, 2016 (the “Order”) pursuant to which the Court ordered that the Trustees of the Trust to direct the Partnership to sell all of the royalty interests owned by the Partnership on or before June 30, 2016.  All remaining matters, including the attorney ad litem’s request for an accounting and the issues concerning termination of the Trust (the “Remaining Matters”), were continued to a later date.  The principal asset of the Trust consists of a 99.99% interest in the Partnership.  In turn, the principal asset of the Partnership is the overriding royalty interest.  As a result of consummation of the sale, the Partnership no longer owns any overriding royalty interest in the Royalty Properties.

The sale was made to Arena Energy, LP and closed on June 24, 2016, but was effective as of February 1, 2016 (the “Royalty Sale”). The Royalty Sale generated $1,830,000 in gross proceeds and occurred as part of the previously announced formal auction process for the overriding royalty interest.  The Trust expects to receive promptly from the Partnership a distribution of approximately $1,756.624, representing 99.99% of the net proceeds from the Royalty Sale of $1,756,800.  Due to the Remaining Matters, the Trust must hold the net proceeds in a segregated account until the Court’s final resolution of the Remaining Matters.  The Remaining Matters are set for trial on November 7, 2016. The disposition of such net proceeds will be made in accordance with the final resolution of the Remaining Matters.

Chevron U.S.A. Inc. (“Chevron”), as the Managing General Partner of the Partnership, engaged EnergyNet.com, Inc. to conduct the marketing process and the related open auction for the overriding royalty interest.  EnergyNet.com, Inc. is a FINRA-registered broker dealer that provides marketing services to the oil and gas industry.  Under its engagement agreement, EnergyNet.com, Inc. is entitled to a 4% commission on the $1,830,000 sale price.

This press release contains forward-looking statements, including statements relating to the Remaining Matters and any disposition of the net proceeds from the Royalty Sale.  Important factors that could cause these statements to differ materially include the outcome of the pending Remaining Matters before the Court, the Trust’s ability to pay its liabilities, and other factors described in the Trust’s Form 10-K for the year ended December 31, 2015 under “Item 1A. Risk Factors,” as well as other risks identified from time to time in its reports on Form 10-Q and Form 8-K as filed with the SEC.  Statements made in this press release are qualified by the cautionary statements made in these risk factors. The Trust does not intend, and assumes no obligations, to update any of the statements included in this press release.

The Bank of New York Mellon Trust Company, N.A.

AS CORPORATE TRUSTEE

CONTACT:  Mike Ulrich

(512) 236-6599

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