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We describe a novel way to implement high-radix crossbar switches. Our work is enabled by a new chip interconnect technology called Proximity Communication (PxC) that offers unparalleled chip IO density. First, we show how a crossbar architecture is topologically mapped onto a PxC-enabled multi-chip module (MCM). Then, we describe a first prototype implementation of a small-scale switch based on a PxC MCM. Finally, we present a performance analysis of two large-scale switch configurations with 288 ports and 1,728 ports, respectively, contrasting a 1-stage PxC-enabled switch and a multi-stage switch using conventional technology. Our simulation results show that (a) arbitration delays in a large 1-stage switch can be considerable, (b) multi-stage switches are extremely susceptible to saturation under non-uniform traffic, a problem that becomes worse for higher radices (1-stage switches, in contrast, are not affected by this problem).