By Luc Cohen and Rory Carroll DALLAS/SAN RAMON, Calif. (Reuters) - Voters at Exxon Mobil Corp's (XOM.N) annual meeting on Wednesday approved a measure to let minority shareholders nominate outsiders for seats on the board, meaning a climate activist could eventually become a director at the world's largest publicly traded oil company. The so-called proxy access measure was the first Exxon shareholder proposal since 2006 to be approved, and it was the only one of 11 proposals related to climate change to pass at meetings held on Wednesday by Exxon and fellow U.S. major Chevron Corp (CVX.N). This year's meetings were arguably the tensest ever, coming on the heels of the Paris accord to curb fossil fuel emissions and as New York's attorney general investigates allegations from environmentalists that Exxon misled the public about climate change risks. Exxon has denied this and complained of being unfairly targeted.