Exxon cited Kandarian’s financial and risk management experience as a reason for adding him to the board, which will now have 11 members.
Exxon does not hedge is oil production but does have insurance and other financial protections for part of its operations.
Shares of Exxon rose 1.9 percent to $88.95 in afternoon trading.
Both Exxon and Chevron are slated to report quarterly results on Friday morning.
Reporting by Ernest Scheyder; Editing by Nick Zieminski