The company said the two directors -- V. Burns Hargis, the president of Oklahoma State University, and Richard Davidson, a former chief executive of Union Pacific -- had tendered their resignations from the board after winning the backing of just slightly more than a quarter of the shareholder votes cast.

"Since (Hargis and Davidson) received the support of approximately 26% and 27%, respectively, of the votes cast, they have tendered their resignations as required by the company’s new majority voting bylaw," Chesapeake said in a statement.

Michael Garland, head of corporate governance for the New York City comptroller, told the annual meeting of investors that "the vote is fundamentally a referendum on the entire board", according to a Reuters report.

The shareholders also soundly rejected the company's executive officer compensation programme, with only 20% backing the measure. However, that vote was only an advisory measure and is not binding.

"Obviously we'll be studying the result of the vote today and see what needs to be done," chief executive Aubrey McClendon told the investor meeting.

Meanwhile, David Dreman -- chairman of Dreman Value Managementm, which owns about 1 million shares in Chesapeake -- told CNBC on Friday that McClendon should either resign or be fired by the company's new board.

"When you see all the things that Aubrey McClendon has done in the past years in increasing numbers, I don't think -- as talented as he is -- he should be a member of Chesapeake anymore," Dreman told the news network. "I think he should be -- either resign or be fired by the reconstructed board."

"I wouldn't buy any more stock at this point," Dreman added.

Shares of Chesapeake, the second-largest US natural gas producer, have lost about half their value over the last year as it seeks to convince its shareholders that it is still a good investment despite steep drops in profits and a spate of corporate governance scandals centred around McClendon.

McClendon has said he will step down as chairman, and Chesapeake has said it will replace four of its current board members with directors chosen by its top shareholders -- activist Carl Icahn and Mason Hawkins' Southeastern Asset Management. This would give shareholder-backed directors a majority of the board.

Chesapeake is under pressure to sell assets and cut spending to cover a $10 billion cash shortfall this year and reduce debt after tumbling natural gas prices have pinched profits.

Earlier on Friday, Chesapeake said it planned to sell its pipeline and related assets to Global Infrastructure Partners for more than $4 billion.

Shares of Chesapeake were up 2.07% at $18.21 at 13:30 in New York.

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Shareholders slap down Chesapeake board