Why do half of S&P 500 firms have duality, that is, a CEO who is also the Chair of the Board? We show theoretically that duality can play an important role in the competition for CEOs. Empirically, we document that duality changes are concentrated at times when new CEOs are hired and firms are more likely to offer duality to CEOs with greater ability. This finding is robust to different measures of CEO ability and types of succession plans. We also show that the correlation between duality and CEO ability is stronger in industries that feature a greater competition for CEOs.