CEO compensation varies widely, even within industries. In this paper, we investigate whether differences in skill explain these differences in CEO pay. Using the idea that skilled CEOs should be more likely to continue prior good performance and more likely to reverse prior poor performance, we develop a new methodology to detect whether skill is related to pay. We find that highly paid CEOs are more skilled than their less well paid peers when pay is performance based and when there is a large shareholder. This detected link between pay and skill is strong even when we examine industry-wide declines: highly paid CEOs are more likely to reverse the firm’s fortunes. We also examine CEO turnovers and show that the firm’s post-turnover performance is related to differences between the two CEO’s pay levels. These results highlight conditions where pay and skill are linked, and hence identify firms where high pay appears to have no justification.