This paper develops a matching model in the market for directors to explain equilibrium board quality. In my model, (1) the boards of directors have the role of monitoring and advising, (2) the impact of a CEO’s quality increases with the size of a …rm under his control, (3) the CEO and the boards could be either complements or substitutes, in the production function, and (4) the boards enjoy money value and reputation value. When the reputation depends on market value of …rms, potential directors like to work at …rms with talented CEOs if they can enjoy enough reputational gain on boards owing to talented CEOs. In contrast, when potential directors want value-added for reputation, they would be at …rms with low-ability CEOs if the CEO and the boards are substitute. My empirical estimates suggest that talented ongoing CEOs and former CEOs work as outside directors of …rms with high market capitalization and with high sales, though not with high assets. The quality of boards is higher where CEO pay is higher, but whether they like to work at …rms with talented CEOs or not is ambiguous due to the endogeneity. The …rms with talented boards would be likely to pay more to CEO. I also …nd that the …rms with high sales pay more to outside directors. A 1% increase in sales makes board compensation increase by 0.66%. Finally, board pay is 0.13% higher where CEO pay is 1% higher. We can infer that the CEO and the boards are complements in the production function.