Combining the companies would be the biggest deal the energy industry has ever seen. It would create a giant with a market capitalization of more than $350 billion at current valuations, and with more revenue that Saudi Aramco. Exxon and Chevron boast enormous oil and gas production assets both at home in the U.S. and around the world, sizable refining and chemical operations, plus instantly recognizable retail brands.

The size and complexity of a potential merger would make such an undertaking daunting, however. Both companies trace their lineage back to the mighty Standard Oil, the monopolistic oil producer run by John D. Rockefeller, which was broken up by the U.S. government. Antitrust authorities around the world would need to weigh the position a merged Exxon and Chevron would have in both the upstream and downstream sectors.

Exxon and Chevron declined to comment on the Dow Jones report.

Still, the benefits of a deal in the current environment are clear. The oil crash of 2020 was sobering for the industry, forcing it to make aggressive spending cuts. Exxon and Chevron weren’t immune. As the flurry of U.S. takeovers in the shale patch late last year showed, investors have cautiously welcomed consolidation as a way to cement lower costs.

That’s one reason why a merger between the two U.S. oil giants makes sense, industry analyst Paul Sankey at Sankey Research wrote in an October note to clients.

“Chevron for ExxonMobil is a great idea,” he said. “It would be a truly bottom of the cycle, counter-cyclical move of the kind the equity market is more-or-less demanding.”

Energy companies are among the worst performers on the S&P 500 index in the past year. Exxon declined 30%, while Chevron dropped 23%, compared with the 13% gain in the benchmark index.