The cumulative reaction probability (CRP) (the Boltzmann average of which is the thermal rate constant) has been calculated for the reaction H-2+OH <--> H2O+H in its full (six) dimensionality for total angular momentum J=O. The calculation, which should be the (numerically) exact result for the assumed potential energy surface, was carried out by a direct procedure that avoids having to solve the complete state-to-state reactive scattering problem. Higher angular momenta (J > 0) were taken into account approximately to obtain the thermal rate constant k(T) over the range 300 < T < 700 K; the result is significantly larger than the experimental values (a factor of approximately 4 at 300 K), indicating that a more accurate potential energy surface is needed in order to provide a quantitative description of this reaction.