We develop a wave packet approach to treating the electronically nonadiabatic reaction dynamics of O(D-1) + H-2 --> OH + H, allowing for the 1(1)A' and 2(1)A' potential energy surfaces and couplings, as well as the three internal nuclear coordinates. Two different systems of coupled potential energy surfaces are considered, a semiempirical diatomics-in-molecules (DIM) system due to Kuntz, Niefer, and Sloan, and a recently developed ab initio system due to Dobbyn and Knowles (DK). Nonadiabatic quantum results, with total angular momentum J = 0, are obtained and discussed. Several single surface calculations are carried out for comparison with the nonadiabatic results. Comparisons with trajectory surface hopping (TSH) calculations, and with approximate quantum calculations, are also included. The electrostatic coupling produces strong interactions between the 1(1)A' and 21A' states at short range (where these states have a conical intersection) and weak but, interestingly, nonnegligible interactions between these states at longer range. Our wave packet results show that if the initial state is chosen to be effectively the 1A' state (for which insertion to form products occurs on the adiabatic surface), then there is very little difference between the adiabatic and coupled surface results. In either case the reaction probability is a relatively flat function of energy, except for resonant oscillations. However, the 2A' reaction, dynamics (which involves a collinear transition state) is strongly perturbed by nonadiabatic effects in two distinct ways. At energies above the transition state barrier, the diabatic limit is dominant, and the 2A' reaction probability is similar to that for 1A ", which has no coupling with the other surfaces. At energies below the barrier, we find a significant component of the reaction probability from long range electronic coupling that effectively allows the wave packet to avoid having to tunnel through the barrier. This effect, which is observed on both the DIM and DK surfaces, is estimated to cause a 10% contribution to the room temperature rate constant from nonadiabatic effects. Similar results are obtained from the TSH and approximate quantum calculations.