We address the problem of steady-state simulation for metastable continuous-time Markov chains with application to stochastic chemical kinetics. Such systems are characterized by the existence of two or more pseudo-equilibrium states and very slow convergence towards global equilibrium. Approximation of the stationary distribution of these systems by direct application of the Stochastic Simulation Algorithm (SSA) is known to be very inefficient. In this paper, we propose a new method for steady-state simulation of metastable Markov chains that is centered around the concept of stochastic complementation. The use of this mathematical device along with SSA results in an algorithm with much better convergence properties, that facilitates the analysis of rarely switching stochastic biochemical systems. The efficiency of our method is demonstrated by its application to two genetic toggle switch models.