Adaptive modulation and coding (AMC) has been adopted in the 3GPP standard in order to improve spectral efficiency. In order to increase the granularity of the adaptation and to provide higher bit rates, multicode transmission is employed. Since the use of AMC requires knowledge of the channel state, the accuracy of this information is important. In practice, errors in estimating the channel state are inevitable, resulting in performance degradation. The average bit rate performance of AMC with multicodes is studied for a CDMA system experiencing Nakagami fading and channel estimation errors. The results are obtained in terms of the generalized Marcum Q-function. Numerical results are provided to illustrate the performance degradations due to inaccuracies in estimating the channel.