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The Chernoff bound is used to estimate the performance of a direct sequence spread spectrum communication system operating over a frequency-selective Rician fading channel. In addition to the degradation caused by the selectivity of the channel, the system is further degraded by the presence of a tone interfering signal. A closed form expression for the bound is presented, and it is seen that at low probabilities of error, the bound appears to be within 1 dB or so of the true value. Numerical results are also presented for typical combinations of system parameters.