This paper considers a large CDMA random access system where a number of users randomly access a basestation through a common CDMA channel. The number of users and spreading gain tend to infinity with their ratio convergent to a constant. An approach is proposed to exploitation of retransmission diversity. Performance of three systems is analyzed: (i) random spreading with exploitation of retransmission diversity; (ii) randomly selected but fixed spreading for each packet with exploitation of retransmission diversity; and (iii) random spreading without exploitation of retransmission diversity. Lower bounds on the limit SIRs of the first two systems and the exact limit SIR of the third system are obtained. User throughput, packet delay, transmission time, and waiting time as well as spectral efficiency in the limit system are obtained as functions of medium access control (MAC). The analytical results are confirmed by simulations. It is shown that out of many system settings, (i) is the most favorable in terms of maximization of spectral efficiency and simplicity of MAC.