Exxon Mobil and Chevron are battling this week over rights to one of the world’s most coveted oil projects, a contest that has chilled the relationship between their senior executives and threatens to upend the industry’s hierarchy.

Exxon’s move last year to derail Chevron’s $53 billion purchase of Hess rankled Chevron’s senior executives and damaged a once-amicable relationship between the two rivals, people familiar with the matter said.

Exxon CEO Darren Woods and Chevron CEO Mike Wirth occasionally dined together and spoke by phone about their joint interests in projects around the world. That relationship has chilled, the people said.

The dispute hinges on Exxon’s claim that it has a contractual right to pre-empt Chevron’s bid for Hess’s stake in a major oil project in Guyana. And it has delayed what would be Chevron’s biggest-ever deal for more than 18 months. Chevron and Hess say Exxon doesn’t have the right to interfere in the corporate acquisition. Talks failed, and Exxon filed for arbitration last year.