We study the structure of optimal wealth and labor income taxes in a Mirrlees economy in which the productivity of labor (i.e., skill) is private, stochastic, and endogenous. Individual agents' skills are determined by their level of human capital. Human capital is not publicly observable and the returns to human capital investment are subject to idiosyncratic shocks. Preferences are not assumed to be additively separable in consumption and human capital investment and, thus, the intertemporal marginal rates of substitution of consumption are private information. We characterize the optimal allocation and a tax system that implements this allocation in equilibrium. The optimal allocation does not satisfy the "reciprocal Euler equation" of Rogerson [Econometrica, 1985], which holds in Mirrlees economies with exogenous skills. The tax system we use in our decentralization of the optimum consists of a wealth tax that is linear in wealth and a labor income tax that depends solely on labor income. The result of Kocherlakota [Econometrica, 2005], establishing the optimality of zero expected marginal wealth tax rate, holds in our model. We show that endogenous skill determination affects the volatility of marginal wealth taxes rather than their expectation. Relative to economies with exogenous skills, the optimal marginal wealth tax rate is more volatile in our endogenous skill economy. Also, we demonstrate the optimality of a wedge in the returns on the two assets present in our economy: At the optimum, the marginal return on human capital investment is strictly larger than the marginal return on physical capital investment.