Chaotic synchronization is treated within the framework of information theory. It is shown that information theory implies fundamental limits to chaotic synchronization in the presence of channel noise. With regard for these limits, a scheme is suggested for the synchronization of two-dimensional chaotic maps. The central idea is that the communication channel should convey a symbolic sequence that contains information about the drive signal. It is established by computer simulations that the scheme enables one to obtain the highest synchronization quality and noise immunity.