The wavevector-dependent shear viscosity, eta(k), is evaluated for a range of temperatures in a supercooled binary Lennard-Jones liquid. The mode coupling theory of Keyes and Oppenheim (Phys. Rev. A 1973, 8, 937) expresses the self-diffusion constant, D, in terms of eta(k). Replacing eta(k) with the usual viscosity, eta = eta(k = 0), yields the Stokes-Einstein law. It is found that the breakdown of the SE law in this system is well described by keeping the simulated k-dependence. Simply put, bath processes on all length scales (wavevectors) contribute to D, the system is much less viscous at finite k, and thus D exceeds the SE estimate based upon eta. The functional form of eta(k) allows for the estimation of a correlation length that grows with decreasing T.