In binary FM-Differential Chaos Shift Keying (FM-DCSK), each information bit is mapped to a frequency modulated chaotic waveform. Because of the inherently broadband nature of chaotic signals, chaotic modulation schemes have potentially better performance in multipath environments than modulation schemes based on sinusoids. However, the multipath performance of chaotic communications systems has not yet been evaluated. This calculation requires an ultra-fast computer simulator. If the computer simulation is performed directly in the RF domain, then a very high sampling frequency has to be used due to the high RF carrier frequency. In this paper, the RF carrier is removed by applying the analytic signal approach, and a low-pass equivalent model is developed for the FM-DCSK system. An ultra-fast simulator based on this model and working in the Matlab environment is shown. Finally, the performance of an FM-DCSK system in a multipath environment is determined by means of the simulator introduced here.