Unsteady, three-dimensional, supersonic flow with nonequilibrium chemistry in a square channel with transverse hydrogen injection was numerically investigated. To this end, the concepts of large-eddy simulation were applied to a model supersonic combustion chamber using a three-dimensional solver of the compressible Navier-Stokes equations with chemical reactions developed by the present authors. The time-accurate computation was accelerated by an implicit method and implemented on a massively parallel computer. The results of the present three-dimensional simulation were analyzed with respect to their timewise behavior and compared, where applicable, with two-dimensional predictions and experimental data obtained by other investigators.