A performance of the complex chaotic spreading sequences with constant power is investigated in a chip-synchronous complex CDMA with a complex scrambling. We estimate a signal-to-interference ratio (SIR) and a bit error rate (BER). An exact invariant measure of the complex chaotic spreading sequence can be obtained. Therefore, the SIR can be calculated analytically. The result can be used as one of the criteria for evaluating the performance of the complex CDMA using the chaotic spreading sequences.