In this letter, we derive a closed-form bit error rate (BER) of M-ary differential chaos shift keying (M-DCSK) systems over multipath Rayleigh fading channels via approximating Gaussian Q-function by polynomials. The approximation is made piece-wisely using polynomials of different degrees and Remez algorithm is applied to achieve the minimax approximation. Our method can be extended into the existing non-coherent transmit-reference chaos-based modulation systems, e.g., short-reference DCSK and multi-carrier DCSK systems. The derived closed-form BERs are compared with the simulated ones in order to verify the efficiency of proposed approximation scheme.