No, a CEO cannot fire a chairman under normal circ*mstances. CEOs can certainly conspire to have unfavorable board members removed, including the chairman, but a CEO is not usually able to unilaterally decide that the chairman will be removed.
One caveat: a CEO who is a majority shareholder might be able to fire board members at will, including the chairman, depending on the board's internal voting system. However, to do so without the backing of other corporate leadership would almost certainly spell widespread panic among investors and other board members.
One caveat: a CEO who is a majority shareholder might be able to fire board members at will, including the chairman, depending on the board's internal voting system. However, to do so without the backing of other corporate leadership would almost certainly spell widespread panic among investors and other board members.