Synchronization between two identical chaotic systems (drive and response) with different initial conditions can be achieved provided that the conditional Lyapunov exponents are all negative. Adding an AM signal to the drive system, the two systems become asymptotically synchronized. The AM signal can be recovered by utilizing the property of the asymptotic synchronization. Chaotic AM noise is present as a direct result of the chaotic AM demodulation. Signal-to-chaotic-AM-noise ratio is calculated as a function of the signal amplitude.