We report the first-principles computation of rate constants for the atmospheric reaction OOH + H -> H-2 + O-3(2) by combining variational transition state theory (VTST) and high-level electronic structure theory. Using the direct dynamics approach, the rate constants were computed, directly, using ab initio electronic structure theory at the second-order many-body perturbation theory (MBPT(2)) and coupled-cluster singles-and-doubles with a perturbative triples correction (CCSD(T)) levels, and variational transition state theory including tunneling. The computed room-temperature rate constant, 6.85 x 10(-12) cm(3) molecule(-1) s(-1), is in excellent agreement with experiment (6.96 x 10(-12)). However, we do not find that the rate constant is nearly constant over the temperature range 250 less than or equal to T less than or equal to 300 K as suggested by experiment. In addition, the calculations suggest the reaction is non-Arrhenius over both the temperature ranges 150-400 It and 150-800 K. The computed temperature dependence of the rate constant is well represented by the three-parameter fit: k = (6.99 x 10(-15)) T-1.10 exp(187/T).