This letter considers multicarrier CDMA systems using rectangular chip waveform, where each user's data stream is serial to parallel converted to a number of lower rate streams. Each lower rate stream is then spread by a random spreading code and a suitable chip rate before modulating orthogonal carriers. It is shown that, for a fixed system bandwidth and a given number of carriers, there exists an optimal carrier spacing that minimizes the multiple access interference. Numerical examples also show that the multicarrier DS-CDMA system previously proposed in performs very close to the muticarrier CDMA system using the optimal carrier spacing.