We present a work-optimal randomized algorithm for simu- lating a shared memory machine (PRAM) on an optical com- munication parallel computer (OCPC). The OCPC model is motivated by the potential of optical communication for par- allel computation. The memory of an OCPC is divided into modules, one module per processor. Each memory module only services a request on a timestep if it receives exactly one memory request. Our algorithm simulates each step of an n lg lg n-processor EREW PRAM on an n-processor OCPC in O(lg lg n) expected delay. (The probability that the delay is longer than this is at most n for any constant a.) The best previous simu- lation, due to Valiant, required (lg n) expected delay.