This paper develops a simple equilibrium model to explain the significant increase in CEO pay in the United States between 1980 and 2003. The model assumes that CEOs have different levels of managerial talent and are matched to firms competitively. In market equilibrium, a CEO's pay changes proportionally with the aggregate firm size, while changing much less with the size of his own firm. The model predicts that the sixfold increase in CEO pay during this period can be fully attributed to the six-fold increase in market capitalization of large US companies. The model also finds that CEO talent dispersion is very small, yet justifies large pay differences. Empirical evidence supports the model, showing that firm size explains many patterns in CEO pay across firms, over time, and between countries. The paper concludes by calibrating the model, which could guide future quantitative models of corporate finance.This paper develops a simple equilibrium model to explain the significant increase in CEO pay in the United States between 1980 and 2003. The model assumes that CEOs have different levels of managerial talent and are matched to firms competitively. In market equilibrium, a CEO's pay changes proportionally with the aggregate firm size, while changing much less with the size of his own firm. The model predicts that the sixfold increase in CEO pay during this period can be fully attributed to the six-fold increase in market capitalization of large US companies. The model also finds that CEO talent dispersion is very small, yet justifies large pay differences. Empirical evidence supports the model, showing that firm size explains many patterns in CEO pay across firms, over time, and between countries. The paper concludes by calibrating the model, which could guide future quantitative models of corporate finance.