In this paper, a backstepping design is proposed to achieve stabilization and synchronization for the Lorenz-Stenflo (LS) chaotic system. The proposed method is a recursive Lyapunov-based scheme and provides a systematic procedure to design stabilizing controllers. The proposed controller enables stabilization of the chaotic motion and synchronization of two identical LS chaotic systems using only a single control input. Numerical simulations are presented to validate the proposed method.