The Chairman of the Board (of Directors) of a company, is (or should be) the chief representative of the shareholders. The CEO of the company, should be, by definition, the leader of the managers.
Combining the two roles in the same person creates an inherent conflict of interest (in most cases).
The job of the chairman of the board is to look out for the shareholders. Or to be more exact, it is to head a board that looks out for the shareholders. A board's main job is to fire incompetent managers, and&... restrain competent ones that overreach. Also, the board should be on the look-out for new talent that might be profitably added to the company's "roster."
A CEO's job is 1) to manage, and 2) to report to a board that sets policies and priorities based on shareholders' needs and wishes (e.g. for either higher income or capital gains, for safety, or a high-risk, high-reward growth policy). A CEO should also look out for the interests, salary, and even "perks," of managers. But one who's also chairman is basically reporting to himself or herself.
The example of Warren Buffett is arguably the exception that proves the rule. In his role has manager of Buffett Partnerships, he was a major shareholder of a number of public corporations, incluidng American Express, in the 1960s. He became "chairman" of Berkshire Hathaway, but turned into a holding company that was basically an extension of his earlier hedge fund.
Problem is, Berkshire Hathaway has since morphed into a major operating company in its own right. It is no longer "just" an investment operation. Mr. Buffett is s... the chief investment officer and chairman. That's only fair. But he might do well to name a CEO of all non-investment operations.
Apparently, he wants to wait until he leaves to do this. Then there would be three successors. There would be a new CEO and CIO, and his son, Howard, would be non-executive Chairman of the Board. Howard Bufffet is a not-always successful executive of various enterprises, who has nevertheless consistently been an honest and forceful advocate of the public interest. He'd be admirable in the "chief shareholder" role--and probably none of the others.
Another "family business" that should probably be chaired by a family member is Ford Motor Co. The Ford family is the single largest shareholder, after all. But it is to his chagrin that Bill Ford was dragged into a management role.
A Chairman and CEO have two different and conflicting roles. That's why they should be kept separate.
Disclosure: Long BRK/A and BRK/B shares.