Exhibit 99.1

TEL OFFSHORE TRUST

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

919 CONGRESS AVENUE / (800) 852-1422 / AUSTIN, TEXAS 78701

TEL OFFSHORE TRUST ANNOUNCES THERE WILL BE NO FOURTH QUARTER 2012 DISTRIBUTION

AUSTIN, TEXAS DECEMBER 21, 2012—TEL OFFSHORE TRUST announced that there will be no trust distribution for the fourth quarter of 2012 for unitholders of record on December 31, 2012. The Trust has not been able to make a distribution to unitholders for sixteen consecutive quarters, or since January 9, 2009. The financial and operating information included herein for the Trust’s fourth quarter of 2012 reflects financial and operating information with respect to the royalty properties for the months of August, September and October 2012.

Gross proceeds for the royalty properties exceeded development and production costs for the months of August, September and October 2012 by $508,129, or $127,032, net to the entire overriding royalty interest, and $101,626 attributable to the Trust.  This is the first quarter in which gross proceeds from the royalty properties have exceeded development and production costs since the second quarter of 2010.  The excess proceeds, net to the entire overriding royalty interest, were applied to reduce the accumulated excess cost carryforward, which represents the amount by which the aggregate development and production costs for the royalty properties since November 2008 have exceeded the related proceeds of the production.  In addition, during the quarter the accumulated excess cost carryforward was reduced by an adjustment of $381,000 for the insurance proceeds received by Chevron U.S.A., Inc. (“Chevron”), as Working Interest Owner, relating to damages incurred at Eugene Island 339 during Hurricane Ike and by an audit adjustment of $49,792.

Gas revenues recorded by Chevron, as a Working Interest Owner, on its royalty properties increased approximately 42% to $120,818 in the fourth quarter of 2012 from $85,155 in the third quarter of 2012.  Natural gas volumes during the fourth quarter of 2012 increased approximately 5% to 40,399 Mcf from 38,430 Mcf during the third quarter of 2012. The average price received for natural gas increased approximately 35% to $2.99 per Mcf in the fourth quarter of 2012 as compared to $2.22 per Mcf in the third quarter of 2012.

Crude oil and condensate revenues recorded by Chevron, as a Working Interest Owner, on its royalty properties increased approximately 10% to $3,377,201 in the fourth quarter of 2012 from $3,082,887 in the third quarter of 2012. Crude oil and condensate volumes during the fourth quarter of 2012 increased approximately 10% to 32,153 barrels, compared to 29,143 barrels produced in the third quarter of 2012. The average price received for crude oil and condensate decreased approximately 1% to $105.04 per barrel in the fourth quarter of 2012 as compared to $105.79 per barrel in the third quarter of 2012.

Capital expenditures decreased by $2,652,205 in the fourth quarter of 2012 to $42,769, as compared to $2,694,974 in the third quarter of 2012. Operating expenses decreased by $1,226,542 in the fourth quarter of 2012 to $2,745,526 as compared to $3,972,068 for the third quarter of 2012. Chevron has informed the Trust that the estimate of the Trust’s net portion of the aggregate cost to plug and abandon the wells

subject to the overriding royalty interest on Eugene Island 339 as of the third quarter 2012 is approximately $19.8 million, approximately $19.7 million of which had been incurred through fourth quarter 2012.  As discussed above, for the fourth quarter of 2012, under the terms of the conveyance for the royalty properties, gross proceeds for the royalty properties exceeded development and production costs thereof, with the portion of such excess attributable to the Trust’s remaining 20% royalty interest, equal to approximately $101,626. As of October 31, 2012, after applying the net proceeds for the quarter and giving effect to the adjustments described above, the aggregate development and production costs for the royalty properties since November 2008 have exceeded the related proceeds of production from the royalty properties by approximately $6.30 million, net to the Trust’s remaining 20% royalty interest.  As a result, the Trust will not be receiving any net proceeds for the fourth quarter of 2012.  In the fourth quarter of 2010, Chevron U.S.A. Inc. withdrew $4,304,894 from the Special Cost Escrow account of the Working Interest Owners (a reserve fund for certain costs) to cover expenses incurred in connection with the plugging and abandonment of Eugene Island 339, which served to reduce the amount by which development and production costs exceeded the related proceeds from production; however, additional deposits to the Special Cost Escrow account will be required in future periods in accordance with the terms of the underlying conveyance of the royalty if, and when, net proceeds would otherwise be payable on the royalty.  In the fourth quarter of 2012, no dollars were escrowed or released from the Special Cost Escrow account of the Working Interest Owners, leaving a balance of $1,000 in the Special Cost Escrow account.

In 2011, Chevron, as the Managing General Partner of the TEL Offshore Trust Partnership, consummated the sale by the Partnership of 20% of the Partnership’s overriding royalty interest (a 25% net profits interest in certain oil and gas properties), as the Trust needed funds to pay for liabilities of the Trust. The Partnership retained a 20% royalty interest (representing 80% of the original 25%  interest).

As previously reported, in July 2012, the Trustees provided written notice to Chevron that the Trust needed funds to pay for the liabilities of the Trust and therefore instructed Chevron, as the Managing General Partner of the Partnership, to take certain actions involving a potential sale by the Partnership of a portion of its overriding royalty interest (a 20% net profits interest in certain oil and gas properties).   As previously reported, Chevron has been marketing for sale by the Partnership a portion of the Partnership’s overriding royalty interest and bids were due December 12, 2012.At this time, the Trustees have instructed the Partnership to delay any further action regarding a potential sale of a portion of the overriding royalty interest and the Trustees are continuing to evaluate the alternatives available to the Trust. Accordingly,  there can be no assurance that such a sale will be consummated, or that the terms, conditions and timing of any such sale will be acceptable to the Partnership.

Effective for third quarter of 2012, the Trustees unanimously determined to suspend further payments of fees to the Trustees until a date to be determined in the future by the Trustees.  Until a subsequent determination by the Trustees, such suspended fees will be accrued as an expense to the Trust, but will not be paid currently.

This press release contains forward-looking statements.  Although the Managing General Partner of the TEL Offshore Trust Partnership has advised the Trust that the Managing General Partner believes that the expectations contained in this press release are reasonable, no assurances can be given that such expectations will prove to be correct. The Working Interest Owners alone control historical operating data, and handle receipt and payment of funds relating to the royalty properties and payments to the Trust for the related royalty. The Trustees of the Trust cannot assure that errors or adjustments by the Working Interest Owners, whether historical or future, will not affect future royalty income and distributions by the Trust.  Other important factors that could cause these statements to differ materially include delays and

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costs in connection with repairs or replacements of hurricane-damaged facilities and pipelines, including third-party transportation systems, the actual results of drilling operations, risks inherent in drilling and production of oil and gas properties, the Trust’s ability to pay its liabilities and the ability of the Partnership to conclude a sale of a portion of its overriding royalty interest on terms advantageous to the Trust, and other factors described in the Trust’s Form 10-K for the year ended December 31, 2011 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 Securities and Exchange Commission.  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

(800) 852-1422

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