The master-slave synchronization of two chaotic systems that interact over a noisy channel is analyzed from an information theoretic point of view. It is argued that arbitrarily precise synchronization, in the sense of the mean square synchronization error, is possible if the channel capacity is higher than the information production rate of the master system. Thus, even with considerable channel noise, very precise synchronization is possible. This is in contrast to the intuitive idea that synchronization necessarily degrades with increasing noise in the channel. A concrete way to achieve this is demonstrated for the Lozi map.