Tracking control of a nonlinear uncertain Chua's chaotic system is studied. With coordinate transform, Chua's chaotic system is transformed to a general form of a strictfeedback control system. Combining the backstepping method with robust control technology, an adaptive parameter control law for a robust output feedback control scheme is developed for output tracking of nonlinear unknown systems. It is shown that the derived robust adaptive controller based on Lyapunov stability theory can guarantee global uniformly bounded ultimate property for all states of the closedloop system, and lead to tracking error decreasing at exponential speed. The simulation results show the effectiveness of the proposed approach.