Elementary three-atom systems provide stringent tests of the accuracy of ab initio theory. One such important reaction, O((3)P) + H2 ? OH(X(2)?) + H, has eluded detailed experimental study because of its high activation barrier. In this reaction, both the ground-state reactant atom and product diatomic molecule have open-shell character, which introduces the intriguing complication of non-Born-Oppenheimer effects in both the entrance and the exit channels. These effects may be probed experimentally in both the fine-structure and the ?-doublet splittings of the OH product. We have used laser-induced fluorescence to measure OD internal product-state distributions from the analogous reaction of O((3)P) with D2, enabled by a unique high-energy O((3)P) source. We find that the OD (?' = 0) product is rotationally highly excited, in excellent agreement with earlier theoretical predictions. However, the distributions over the OD(X(2)?) fine-structure and ?-doublet states, diagnostic of electronic non-adiabaticity in the reaction, challenge the prevailing theoretical understanding.