We have applied improved canonical and microcanonical variational transition state theories to the calculation of the rate constants for the polyatomic reaction OH+H2→H2O+H over the temperature range 200-2400 K using the Schatz-Elgersma fit to the Walch-Dunning ab initio potential energy surface. The results are compared to canonical variational transition state theory calculations that employed the same potential energy surface and to experiment. We find that the new results, which are in good agreement with experiment, differ very slightly from those obtained with canonical variational theory. One explanation for this agreement is that the microcanonical variational transition states have a rather weak energy dependence and lie within 0.04a0 of the ground-state adiabatic barrier maximum. We also find that quantum mechanical effects and the inclusion of reaction-path curvature are important at lower temperatures, and that the transition state theory treatment of this reaction breaks down for temperatures higher than about 2400 K.