Simulations of translational motion on lattices with spatially heterogeneous dynamics have been performed, Translation occurs by nearest neighbor jumps on a three-dimensional simple cubic lattice. The overall lattice is subdivided into cubic blocks. The rate for jumps within a given block is controlled by the local relaxation time (or rotation time) for that block. Blocks exchange their local relaxation times on a specified time scale. If the local distribution of relaxation times is given by a Kohlrausch-Williams-Watts distribution, the simulation results can reproduce experimental observations of enhanced translational diffusion in supercooled liquids. This adds further weight to arguments that dynamics in deeply supercooled liquids are spatially heterogeneous and that this heterogeneity is responsible for the non-exponential relaxation functions which are often observed. For systems with only two local relaxation times, the simulation results are in good agreement with effective medium theory.