This paper presents an observer-based hybrid adaptive cerebellar model articulation controller (CMAC) with a supervisory controller for uncertain chaotic systems, in which the hybrid adaptive control composed of a direct adaptive CMAC and an indirect adaptive CMAC control is performed as the sliding mode control (SMC). The total states of the chaotic system are not assumed to be available for measurement. A state observer is used to estimate unmeasured states of the systems. The supervised control is appended to assure that the hybrid adaptive CMAC controller achieve a stable closed-loop system through Lyapunov stability theory. Finally, simulation results show that the effect of the approximation error on the tracking error can be attenuated efficiently.