This paper discusses the matching between CEOs of different talent and firms of different size, by considering boards' costly monitoring of CEOs who have private information about firm output. By incorporating a costly state verification model into a matching model, we have a number of novel findings. First, positive assortative matching (PAM) breaks down as larger firms match with less talented CEOs when monitoring is sufficiently costly despite of complementarity in firms' production technology. More importantly, PAM can be the equilibrium sorting pattern for large firms and high talent CEOs even it fails for small firms and low talent CEOs, which implies that empirical applications relying on PAM are more robust by using samples of large firms. Second, under positive assortative matching, CEO compensation can be decomposed into frictionless competitive market pay and information rent. More talented CEOs extract more rent, which makes their wage even higher. Third, firm-level corporate governance depends on aggregate market characteristics such as the scarcity and allocation of CEO talent. Weak corporate governance can be optimal when CEO talent is sufficiently scarce. My analysis yields a number of empirical predictions on equilibrium sorting pattern, CEO compensation, and corporate governance.