Competitive sorting models of the CEO labor market (e.g., Edmans, Gabaix and Landier (2009)) predict that differences in CEO productive abilities, or 'talent,' should be an important determinant of CEO pay. However, measuring CEO talent empirically represents a major challenge. In this paper, we document reliable evidence of pay for CEO credentials and argue that the evidence is consistent with models of the CEO labor market. Our main finding is that boards' compensation decisions reward several reputational, career, and educational credentials of CEOs, with newly-appointed CEOs earning a 5 percent ($280,000) total pay premium for each decile improvement in the distribution of these credentials. Consistent with boards using credentials as publicly-observable signals of CEO abilities, we show that pay for credentials displays key cross-sectional features predicted by theory, such as convexity in credentials and complementarity with firm size. Our main finding is robust to a battery of identification tests that address selectivity and endogeneity concerns, including instrumental variables estimates and controlling for firm and CEO fixed effects. We also show that credentials capture variation in CEO human capital that is different from lifetime work experience, and are positively related to long-term firm performance and board monitoring, which helps to distinguish our results from alternative stories based on CEO general human capital, hype, and entrenchment. Overall, our findings suggest that sorting considerations in the CEO labor market are an important determinant of CEO pay. Our results also suggest that the rise in CEO pay over the last decades may owe at least in part to a rise in the CEO talent premium.