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CEO duality refers to the situation when the CEO also holds the position of the chairman of the board.
The board of directors is set up to monitor managers such as the CEO on the behalf of the shareholders. They design compensation contracts and hire and fire CEOs. A dual CEO benefits the firm if he or she works closely with the board to create value.
Establishing a unity of command at the head of the firm allows the firm to send a reassuring message to shareholders. However, it is also easier for the CEO to assert control of the board and consequently make it more difficult for shareholders to monitor and discipline the management. 
Research in Motion, the maker of Blackberry, has a dual CEO/chairman. In fact, it has two co-chairmen (Mike Lazaridis and Jim Balsillie), who are also co-CEOs, and one of whom is now CMO.