We report the first-principles computation of rate constants for atmospheric reactions, by combining variational transition state theory (VTST) and high-level electronic structure theory. Extending the direct dynamics approach, the rate constants for OH+HCl 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, 7.03 x 10(-13) cm(3) molecule(-1) s(-1), is in good agreement with experiment (8.0 X 10(-13)). The rate constant was computed over the temperature range 138-1055 K. The methods developed in this work are quite general, and can be applied to obtain rate constants for many reactions of interest in atmospheric and combustion chemistry, in the absence of experiment.