We present an overview of the Graphics Processing Unit (GPU)-based spatial processing system created for the Canadian Hydrogen Intensity Mapping Experiment (CHIME). The design employs AMD S9300x2 GPUs and readily available commercial hardware in its processing nodes to provide a cost- and power-efficient processing substrate. These nodes are supported by a liquid-cooling system which allows continuous operation with modest power consumption and in all but the most adverse conditions. Capable of continuously correlating 2048 receiver-polarizations across 400MHz of bandwidth, the CHIME X-engine constitutes the most powerful radio correlator currently in existence. It receives 6.6Tb/s of channelized data from CHIME’s FPGA-based F-engine, and the primary correlation task requires complex multiply-and-accumulate operations per second. The same system also provides formed-beam data products to commensal FRB and Pulsar experiments; it constitutes a general spatial-processing system of unprecedented scale and capability, with correspondingly great challenges in computation, data transport, heat dissipation, and interference shielding.