NON-VON is a highly parallel non-von Neumann supercomputer presently under construction at Columbia University. The basis for NON-VON's significant cost/performance advantage lies in a highly unusual application of VLSI technology to the realization of massive computational parallelism. This paper outlines the manner in which the emerging technology of VLSI circuits is employed in NON-VON to achieve this advantage. Particular emphasis is given to novel aspects of the design, layout, and operation of the NON-VON processing element, eight of which are to be embedded within each integrated circuit chip.