Exhibit 99.1

TEL OFFSHORE TRUST

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

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

TEL OFFSHORE TRUST ANNOUNCES THERE WILL BE NO FIRST QUARTER 2014 DISTRIBUTION

AUSTIN, TEXAS April 11, 2014—TEL OFFSHORE TRUST announced that there will be no trust distribution for the first quarter of 2014 for unitholders of record on March 31, 2014. The Trust has not been able to make a distribution to unitholders for twenty-one consecutive quarters, or since January 9, 2009. Except as disclosed below, the financial and operating information included herein for the Trust’s first quarter of 2014 reflects financial and operating information with respect to the royalty properties for the months of November and December 2013 and January 2014.

Gross proceeds for the burdened royalty properties exceeded development and production costs for the months of November and December 2013 and January 2014 by $426,454, or $106,614, net to the entire overriding royalty interest, and $63,968 attributable to the Trust.  The foregoing sums also include and reflect prior period adjustments as more particularly described below.  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 burdened royalty properties since November 2008 have exceeded the related proceeds of the production.

Gas revenues recorded by Chevron for the quarter on the burdened royalty properties decreased approximately 20% to $92,267 from $116,021 in the fourth quarter of 2013.  The fourth quarter gas revenues included a significant increase as a result of prior period adjustment.  Excluding the impact of the prior period adjustments in each quarter, gas revenues recorded by Chevron for the quarter on the burdened royalty properties increased approximately 1% to $88,321 in the first quarter of 2014 from $87,838 in the fourth quarter of 2013.  Natural gas volumes during the first quarter of 2014 were 20,587 Mcf compared to 22,415 Mcf for the fourth quarter of 2013.  The fourth quarter included a prior period adjustment for Ship Shoal 182/183 that resulted in a decrease of 7,868 Mcf.  Excluding the prior period adjustments for each quarter, natural gas volumes during the first quarter of 2014 decreased approximately 36% to 19,395 Mcf from 30,281 Mcf during the fourth quarter of 2013.  The decrease in production is primarily due to wells being shut in for maintenance work at Ship Shoal 182.  Excluding the impact of prior period adjustments, the average price received for natural gas production increased approximately 57% to $4.55 per Mcf in the first quarter of 2014 from $2.90 per Mcf in the fourth quarter of 2013.

Crude oil and condensate revenues recorded by Chevron for the quarter on the burdened royalty properties decreased approximately 29% to $2,248,374 in the first quarter of 2014 from $3,163,484 in the fourth quarter of 2013.  Crude oil and condensate volumes during the first quarter of 2014 decreased approximately 48% to 22,568 barrels, compared to 43,164 barrels during the fourth quarter of 2013.  Excluding the impact of prior period adjustments, which had the effect of increasing the recorded volume in the fourth quarter by 7,580 barrels, crude oil and condensate volumes during the first quarter of 2014 decreased approximately 37% to 22,563 barrels, compared to 35,583 barrels reported in the fourth quarter of 2013.  The decrease in production is primarily due to wells being shut in for maintenance work at Ship Shoal 182.  Excluding the impact of

prior period adjustments, the average price received for crude oil and condensate production decreased approximately 9% to $98.95 per barrel in the first quarter of 2014 as compared to $108.44 per barrel in the fourth quarter of 2013.

Capital expenditures increased by $4,023 in the first quarter of 2014 to $141,634, as compared to $137,611 in the fourth quarter of 2013. Operating expenses increased by $716,215 in the first quarter of 2014 to $1,688,559 as compared to $972,344 for the fourth quarter of 2013.

As previously disclosed, during September 2008, the platforms, wells and infrastructure associated with the Eugene Island 339 field were completely destroyed by Hurricane Ike.  While Chevron has completed the work it deemed required to clear the remaining infrastructure and abandon those wells, platforms and infrastructure, the interruption in production and the plugging and abandonment costs, each related to the Eugene Island 339 field, were the primary contributors to the resulting excess of development and production costs over proceeds of production.  Chevron has informed the Trust that the estimate of the Trust’s net portion of the aggregate cost to plug and abandon the wells, remove and abandon platforms and infrastructure and remediate the surface subject to the overriding royalty interest on Eugene Island 339 as of October 31, 2013 remains at approximately $19.8 million.  Of this amount, approximately $19.76 million has been incurred through March 1, 2014.  While this work may be complete, additional vendor invoices for this work may be received in the future, which expenses will or could bear upon the proceeds which may be received from Eugene Island 339.

As discussed above, gross proceeds for the royalty properties for the first quarter of 2014 exceeded development and production costs thereof, with the portion of such excess attributable to the Trust’s interest in the remaining 15% royalty interest equal to approximately $63,968.  As of January 31, 2014, after applying the net proceeds for the months of November and December 2013 and January 2014, the amount by which the aggregate development and production costs for the royalty properties since November 2008 have exceeded the related proceeds of production from the royalty properties has been reduced to approximately $4.9 million (or approximately $3 million, net to the Trust’s interest in the remaining 15% royalty interest) as compared to $5 million (or approximately $3 million, net to the Trust’s interest in the remaining 15% royalty interest) as of October 31, 2013. The Trust will not receive any distribution of net proceeds until such time as the proceeds of production exceed the accumulated excess cost carryforward. As a result, the Trust will not be receiving any net proceeds for the first quarter of 2014.

As previously reported, in 2011, Chevron, as the Managing General Partner of the TEL Offshore Trust Partnership (the “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) to RNR Production, Land and Cattle Company, Inc. (“RNR Production”), as the Trust needed funds to pay for liabilities of the Trust.

As also previously reported, on October 31, 2013, Chevron, as the Managing General Partner of the Partnership, consummated a sale of 25% of the Partnership’s remaining overriding royalty interest (or 5% of 8/8ths) and retained 60% of the original overriding royalty interest (or 15% of 8/8ths). On November 25, 2013, the Trust used $300,000 from the net proceeds from the October 2013 royalty sale to repay the principal amount of the Trust’s indebtedness to the Bank of New York Mellon, N.A. under the demand promissory note dated May 23, 2013 in the original principal amount of $300,000 executed by the Trust.

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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 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 other factors described in the Trust’s Form 10-K for the year ended December 31, 2013 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:  Michael J. Ulrich

(512) 236-6599

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