Market capitalisation of BP was $131.2 billion, based on Friday's closing share price, compared with $131.3 billion for Chevron
BP's shares dipped 0.11 percent on Monday, while Chevron shares traded down 0.8 percent. However, a fall in sterling against the dollar meant BP's market value fell more.
The collapse in crude prices from a record above $147/barrel in July to around $63/barrel on Monday has dented confidence in the oil sector.
BP's exposure to Russia - its TNK-BP joint venture accounts for a quarter of BP's oil and gas production - has weighed on the stock.
In September, BP resolved a dispute with its Russian partners in TNK-BP over control of the unit by conceding some control to the billionaires.
This eased worries that BP might lose its half share of the business altogether but a collapse in Russian shares and worries about Russian relations with the West after the Georgian conflict in August has weighed on BP's shares.
BP was the industry's number two until it was overtaken by Royal Dutch Shell in 2006, after BP's valuation was hit by the Texas City refinery explosion in 2005, which killed 15 workers, and by big project delays.
BP's value has hovered around the same level as Chevron's in recent months a BP spokesman said, but he could not confirm if or when Chevron had previously risen above BP's market value.