Thermal diffusion rates of hydrogen atoms in a face-centered cubic (fee) xenon lattice have been computed at 12, 40, and 80 K using a classical variational transition-state theory method which employs a Markov walk/damped trajectory procedure to effect convergence. The two-body Xe/H interaction is obtained from the results of ab initio calculations at the Moller-Plesset fourth-order perturbation theory level with ah configurations through quadruples included. The calculations employ a double-zeta basis set combined with two different pseudopotentials for the xenon core. Pairwise potentials are generated by fitting the ab initio results to a Lennard-Jones (12,6) potential. Standard combining rules are also employed to obtain the Xe/H pairwise interaction as a test of such procedures. The calculations show that thermal diffusion rates of hydrogen atoms in fee xenon crystals are very slow with an activation energy between 2-3 kcal/mol. The diffusion rates are observed to increase with increasing temperature, as expected. Hydrogen atom tunneling is the major diffusion process at temperatures around 12 K. At the higher temperatures studied, tunneling is negligible. Comparison of the results with measured diffusion coefficients indicates that nearly all of the experimentally observed diffusion is occurring along lattice defects, grain boundaries, vacancies, and other lattice imperfections.