New generation radio interferometers encode signals from thousands of antenna feeds across large bandwidth. Channelizing and correlating this data requires networking capabilities that can handle unprecedented data rates with reasonable cost. The Canadian Hydrogen Intensity Mapping Experiment (CHIME) correlator processes 8-bits from N=2048 digitizer inputs across 400~MHz of bandwidth. Measured in \(N^2~\times \) bandwidth, it is the largest radio correlator that has been built. Its digital back-end must exchange and reorganize the 6.6~terabit/s produced by its 128 digitizing and channelizing nodes, and feed it to the 256-node spatial correlator in a way that each node obtains data from all digitizer inputs but across a small fraction of the bandwidth (i.e. `corner-turn'). In order to maximize performance and reliability of the corner-turn system while minimizing cost, a custom networking solution has been implemented. The system makes use of Field Programmable Gate Array (FPGA) transceivers to implement direct, passive, full-mesh, high speed serial connections between sixteen circuit boards in a crate, to exchange data between crates, and to offload the data to a cluster of 256 graphics processing unit (GPU) nodes using standard 10~Gbit/s Ethernet links. The GPU nodes complete the corner-turn by combining data from all crates and then computing visibilities. Eye diagrams and frame error counters confirm error-free operation of the corner-turn network in both the currently operating CHIME Pathfinder telescope (a prototype for the full CHIME telescope) and a representative fraction of the full CHIME hardware providing an end-to-end system validation. An analysis of an equivalent corner-turn system built with Ethernet switches instead of custom passive data links is provided.