ExxonMobil is trying to put a stop to Chevron Corp. and its bid to enter the lucrative Guyanese offshore oil and natural gas patch.

The company has filed for arbitration, claiming Chevron’s bid to snap up Hess Corp.’s Guyana assets goes against a contract clause that grants ExxonMobil a right of first refusal.

Last October, Chevron said it was buying Hess in an all-stock transaction valued at $53 billion. Guyana was seen as the crown jewel in the deal. Chevron CEO Craig Wirth said at the time that Guyana’s discoveries were set to “underpin further growth into the 2030s.”

The Guyana offshore consortium is led by ExxonMobil and operated by affiliate Esso Exploration and Production Guyana Ltd. with a 45% stake. Hess Guyana Exploration Ltd. holds a 30% interest, and...