Recently, multicarrier transmission schemes have been introduced into code-division multiple access (CDMA) systems to gain advantages for high data rate transmission. One of the methods is to transmit identical narrowband direct-sequence (DS),waveforms in parallel over a number of subchannels using frequency diversity, In this paper, we propose a multicarrier CDMA sg-stem with an adaptive subchannel allocation method for forward links. In the proposed system, instead of identical DS waveforms being transmitted over a number of subchannels in parallel, each user's DS waveform is transmitted over the user's favorite subchannel which has the largest fading amplitude among all the subchannels. We analyze the performance characteristics of the system when orthogonal and random signature sequences are used. The proposed system is shown to have performance gain over the conventional multicarrier CDMA system. We also investigate how the performance is influenced when the signal is not perfectly allocated into the best subchannel.