The collisionally induced random particle velocities in a rapid granular shear flow drive the diffusion of particles in manner directly analogous to the thermal diffusion of molecules or the eddy-induced diffusion in a turbulent flow. This paper reports measurements, via computer simulation, of the anisotropic diffusion tensor for a granular shear flow. The components are determined both by particle tracking and through velocity correlations, which are found to agree with reasonable accuracy. As might be expected from symmetry arguments, there are four non-zero components generated in a simple shear flow: the three diagonal components and one off-diagonal component.