Most board chairs are experienced leaders. Half the chairs of the S&P 500 double as their companies’ chief executives, and the vast majority of the rest are former CEOs. But the close association of the two positions creates problems. It’s difficult for a board led by the CEO to serve as a check on that CEO—which is precisely why, after the corporate scandals of the 1990s and early 2000s, more companies began separating the roles. However, that division can create another problem: When the chair is not the CEO, there’s a real danger that he or she will start acting as an alternative chief executive, sowing conflict and confusion among the firm’s top managers.