The worldline quantum Monte Carlo method is a computational technique for studying the properties of many-electron and quantum-spin systems. In this paper, our efforts in developing an efficient implementation of this method for the massively parallel Connection Machine CM-2 are described. Why one must look beyond the obvious parallelism in the method in order to reduce interprocessor communication and increase processor utilization, and how these goals may be achieved using a plaquette-based data representation are discussed. Performance statistics for the implementation and sample calculations for the spinless fermion model are also presented.