The fading wire-tap channel is investigated, where the source-to-destination channel and the source-to-wire-tapper channel are corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information is assumed to be known at both the transmitter and the receiver. The parallel wire-tap channel with independent subchannels is first studied, which serves as an informationtheoretic model for the fading wire-tap channel. Each subchannel is assumed to be a general broadcast channel and is not necessarily degraded. The secrecy capacity of the parallel wire-tap channel is established, which is the maximum rate at which the destination node can decode the source information with small probability of error and the wire-tapper does not obtain any information. This result is then specialized to give the secrecy capacity of the fading wire-tap channel, which is achieved with the source node dynamically changing the power allocation according to the channel state realization. An optimal source power allocation is obtained to achieve the secrecy capacity. This power allocation is different from the waterfilling allocation that achieves the capacity of fading channels without the secrecy constraint.