The companies are in talks on Exxon's claim it has a right to first refusal of any sale of the Stabroek block, a giant field off the coast of Guyana that contains at least 11 billion barrels of oil.
The dispute between the top U.S. oil producers could end Chevron's $53 billion deal for Hess, Chevron warned in a securities filing. If the deal falls part, Hess could be liable for a $1.7 billion breakup fee.
Hess shares fell more than 3% in late trading. Chevron fell almost 1%.
Exxon said in a statement it wants to ensure it will "preserve our right to realize the significant value we’ve created and are entitled to in the Guyana asset," adding it is "working closely with the Guyanese government to ensure their rights and privileges."
"You have to assume that Chevron made a business decision that Exxon wouldn't try to preempt," said Dan Pickering, chief investment officer at Pickering Energy Partners.
