UPDATE 1-Glass Lewis backs Exxon CEO/Chmn split

(Changes attribution, adds background and details from report)

NEW YORK, May 13 (Reuters) - Proxy advisory firm Glass Lewis has recommended Exxon Mobil Corp (XOM.N: Quote, Profile, Research, Stock Buzz) shareholders vote in favor of separating the company's chairman and chief executive positions, adding to a growing chorus of voices calling for the split.

Glass Lewis said in a report issued on Monday that an independent chairman would be "better able to oversee the executives of the company and set a pro-shareholder agenda without the management conflicts that a CEO or other executive insiders often face."

Rex Tillerson currently holds both jobs.

The proposal to split the positions has drawn media attention as many members of the Rockefeller family have publicly supported the move. John D. Rockefeller founded Standard Oil Co in 1870, and it became a precursor to Exxon Mobil.

Top proxy advisory firm ISS, a unit of RiskMetrics Group, has also recommended shareholders vote in favor of separating the positions.

Exxon has said that the board believes that the most effective leadership structure for the company right now is for Tillerson to serve as both chairman and CEO. It said it believes the decision as to who should serve as chairman and chief executive officer is the proper responsibility of the board.

The company sent an e-mail to institutional investors on Monday lobbying them to vote against the proposal, as well as one that would give shareholders an advisory vote on executive pay.

Both proposals are nonbinding.

The company may be feeling the heat on executive pay, as investors holding 41.2 percent of the voted shares supported a similar proposal last year. Shareholders with about 40 percent of the voted shares backed splitting the chairman and chief executive positions in 2007. (Reporting by Michael Erman; editing by John Wallace and Dave Zimmerman)