The first quantum-state-resolved distributions over the full range of available product levels are reported for any isotopic variant of the elementary reaction of O((3)P) with molecular hydrogen. A laser-detonation source was used to produce a hyperthermal oxygen-atom beam, which allowed for sufficient collision energy to surmount the reaction barrier. This beam was crossed by a supersonic beam of D2. The nascent OD products were detected by laser-induced fluorescence. OD rotational distributions in vibrational states v' = 0, 1, and 2 at a collision energy of 25 kcal mol(-1) are reported, together with distributions for the dominant product vibrational level, v'= 0, at lower collision energies of 20 and 15 kcal mol(-1). The OD product is highly rotationally excited, to a degree that declines as expected for the higher vibrational levels or for reductions in the collision energy. The measured rovibrational distributions at the highest collision energy are in excellent agreement with previous theoretical predictions based on quantum scattering calculations on the triplet potential energy surfaces developed by Rogers et al. (J. Phys. Chem. A 2000, 104, 2308-2325). However, no significant OD spin-orbit preference was observed, in contrast to the predictions of most existing theoretical models of the non-adiabatic dynamics based on the widely used reduced-dimensional four-state model of Hoffmann and Schatz (J. Chem. Phys. 2000, 113, 9456-9465). Furthermore, a clear observed preference for OD Π(A') Λ-doublet levels is not consistent with a simple extrapolation of the calculated relative reaction cross sections on intermediate surfaces of (3)A' and (3)A″ symmetry.