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A tracker is proposed for reconstructing the transmitted chaotic signal under the practical condition of the transmitted signal being contaminated by noise and its generating function being subject to strong parameter variations. This tracker uses a modified radial-basis-function (RBF) neural network which incorporates a learning algorithm for tracking the noisy chaotic signal under parameter variations. Using this tracker, a non-coherent detector is designed for demodulating chaos-shift-keying (CSK) signals in a CSK digital communication system. Computer simulations, in which Chua's circuit is used a the chaos generator, are presented to demonstrate the tracking ability and CSK demodulation of the proposed method.