This paper addresses the problem of optimal predefined-time stability. Predefined-time stable systems are a class of fixed-time stable dynamical systems for which the minimum bound of the settling-time function can be defined a priori as a explicit parameter of the system. Sufficient conditions for a controller to solve the optimal predefined-time stabilization problem for a given system are provided. These conditions involve a Lyapunov function that satisfy both a certain differential inequality for guaranteeing predefined-time stability and the steady-state Hamilton-Jacobi-Bellman equation for guaranteeing optimality. Finally, this result is applied to the predefined-time optimization of the sliding manifold reaching phase.ITESO, A.C.CINVESTAV-IPN