Code division multiple access (CDMA) over frequency-selective fading channels faces challenges in suppressing multiuser interference (MUI), but can also benefit from the channel-induced multipath diversity. On the other hand, uncoded orthogonal frequency division multiple access (OFDMA) is MUI-free by design, but faces challenges arising from the fading-induced loss of multipath diversity. We wed the advantages of CDMA with those of OFDMA. We design a group-orthogonal multi-carrier CDMA (GO-MC-CDMA) scheme that minimizes MUI subject to the constraint that the full multipath diversity is enabled for all users. Each group of GO-MC-CDMA users shares a properly selected set of system subcarriers. MUI only exists among users in the same small-size group, which renders the application of low-complexity multiuser detection per group practically feasible. Simulation results illustrate the merits of GO-MC-CDMA over competing multi-access alternatives.