The resolution to separate the positions of chairman and C.E.O. is similar to one put forward last year, which received 40 percent of the vote. The Rockefellers said they expected the resolution would do better this year and expressed hope that the board would make changes if the nonbinding resolution received more than 50 percent of the vote.

The Connecticut state pension fund and the two big California public pension funds, Calpers and Calstrs, support the four resolutions. Denise Nappier, the treasurer of the State of Connecticut, said Exxon Mobil is the state pension fund's largest single holding, at $300 million.

As the world's biggest publicly traded company—and biggest nonstate energy producer—Exxon Mobil has long been a lightning rod for critics of many stripes. At its annual meeting, shareholders will be asked to vote on 19 resolutions, most of them concerning the environment and corporate government.

Another reason why Exxon Mobil has been a target was Raymond, its longtime leader and an irascible bull of a C.E.O. who cared little about the niceties of corporate P.R.

That comes across in one of the arguments for the resolution on an independent chairman, brought by Robert Monks, the longtime shareholder activist, in Exxon's own proxy.

It cites part of an exchange between Raymond and the then-state treasurer of Maine, Dale McCormick, at the 2004 annual shareholders meeting.

McCormick: Then may I pose that question to Mr. Houghton, who is the chair of the audit committee?'

Raymond: You may not, you may not.

McCormick: Why, sir?

Raymond: Because that's not—the audit committee looks at the recommendations of management. That's properly the responsibility of the controller of the corporation.

McCormick: May I pose it to you?

Raymond: Oh, sure. You can pose anything to me. (Laughter)

McCormick: Will you answer me then?

Raymond: Oh, that's a different question. (More laughter)

McCormick: Sir, I do not think it is a matter of laughter when an institutional investor representing over 3 million shares cannot get answers to an important question like this.

Raymond: The question is precisely what?

McCormick: What provisions have you made on the financial statements for the damage caused by climate change and the potential liability [resulting therefrom]?

Raymond: It's neither likely nor could it be estimated.