In this paper, we propose a new approach to compute the exact bit error rate expression for asynchronous chaos-based DS-CDMA system over multipath channel. Perfect estimation of the channel coefficients with the associated delays and chaos synchronization are assumed. A simple RAKE receiver structure is considered. A stationary multipath channel with constant gain is assumed. An asynchronous multi-user chaos-based DS-CDMA system is then defined and the BER is derived in terms of the energy distribution, the number of paths, the noise variances, and the number of users.