Thermal rate constants for the H + H2S --> H-2 + SH reaction have been calculated over a temperature range of 100-2500 K using variational transition state theory combined with the multidimensional semiclassical tunneling correction. Potential energy curves for the reaction have been calculated using the spin-projected fourth-order Moller-Plesset perturbation method and quadratic configuration-interaction method with the correlation-consistent polarized valence triple-zeta basis set. The calculated rate constants agree quite well with experiment over a wide range of temperature; in particular, excellent agreement with experiment is obtained around room temperatures. We have thus succeeded in quantitatively predicting the non-Arrhenius temperature dependence of thermal rate constants for the present reaction without adjusting any potential parameters, which has been observed recently by Yoshimura [Chem. Phys. Lett. 189, 199 (1992)] and by Peng, Hu, and Marshall [J. Phys. Chem. 103, 5307 (1999)].