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One of the most serious deterrants to the development of multiple processor architectures has been the problem of providing adequate communication between the discrete processing elements. This thesis examine two communications-based constraints. The first constraint is related to the physical structure of the VLSI chip. The wider the communication path the more pins are needed to effect the data transfer. As Integrated Circuits grow in computational power, more communication capacity is needed, pushing designs closer to the pin limitation of the packaging technology. The second constraint, somewhat related to the first, is the limited speed with which data can be transmitted via internal channels. Typical speeds one can achieve on a single wires are on the order of 1 Gbps. The recent development of an Optoelectronic Multiplexer may allow VLSI chips to communicate at rates up to 7 Gbps. An architecture for a parallel processing computer which takes advantage of this new capability is presented. The feasibility is presented. The feasibility of a single-chip parallel-processor based on the Optoelectronic Multiplexer is examined by projecting current trends in processor speed, power, and transistor count into estimates of throughput for a multi-processor IC.