In this paper, we develop a simple linear feedback controller, which employs only one of the states of the system, to stabilize the modified Chua's circuit to an invariant set which consists of its nontrivial equilibria. Moreover, we show for the first time that the closed loop modified Chua's circuit satisfies set stability which can be considered as a generalization of common Lyapunov stability of an equilibrium point. Simulation results are presented to verify our method.