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This paper provides an accurate analysis of the performance of a random-carrier (RC) code-division multiple-access (CDMA) scheme recently introduced for use in high capacity optical networks. According to this scheme coherent optical techniques are employed to exploit the huge bandwidth of single-mode optical fibers and are coupled with spread spectrum direct sequence modulation in order to mitigate the interference from other signals due to the frequency overlap caused by the instability of the carrier frequency of the laser, or to the mistakes in the frequency coordination and assignment. The average bit error probability of this multiple-access scheme is evaluated by using the characteristic function of the other-user interference at the output of the matched optical filter. Both phase noise and thermal noise are taken into account in the computation. Time-synchronous as well as asynchronous systems are analyzed in this context. Binary phase shift keying (BPSK) and on-off-keying (OOK) data modulation schemes are considered. The analysis is valid for arbitrary values of the spreading gain and the number of interfering users. The performance evaluation of RC CDMA establishes the potential advantage in employing hybrids of wavelength division multiple access (WDMA) and CDMA to combat inter-carrier interference in dense WDMA systems.