A new multicarrier spread spectrum modulation scheme is proposed in this paper. This scheme uses sinusoidal chip waveforms to shape the spectrum of each subcarrier of a multicarrier direct sequence spread spectrum (DS-SS) signal. As a result, each subcarrier has two distinct spectral lobes, one a lower sideband (LSB) and the other an upper sideband (USB). By properly selecting the parameters of the sinusoidal chip waveforms, the two sideband signals can be made to undergo independent fading in a dispersive fading channel. These two independently-faded sideband signals, when combined at the receiver, provide diversity gain to the system. Our analysis and simulation results show that by properly selecting the chip waveform parameter and the intersubcarrier frequency separation, the bit error ratio (BER) performance of the proposed scheme is superior to that of the conventional MC-DS-CDMA system in dispersive fading channels. In addition, spectral sidelobes are naturally reduced by our scheme.