Code-Hopping Multiple Access (CHMA) has been an emerging Multiple Access (MA) technology which offers excellent performance in multipath fading channels with Orthogonal Complementary Codes (OCC). Orthogonality among users is not preserved in multipath channel conditions using the existing orthogonal and semi-orthogonal codes. Further, Multiple Access Interference (MAI) and Multipath Interference (MPI) destroy orthogonality of the code set which in turn increases the error rate during the detection process. An OCC set possesses both ideal auto-correlation and ideal cross-correlation properties for any two codes in the same set. Here, we employ OCC for spreading and prove that the performance of OCC is superior to those of Gold codes in multipath channels where orthogonality does not hold. The error probability expressions for Rayleigh and Nakagami-m fading channels using Maximal Ratio Combining (MRC) are derived for CHMA system using OCCs. We then evaluate the system performance using the proposed technique and show that the new scheme is much better compared to traditional CHMA schemes.