We present a general procedure for studying intersystem crossing effects in bimolecular chemical reactions, along with an application of this to the O + H-2 reaction. In this procedure, we use previously derived singlet and triplet potential energy surfaces that were based on high quality multireference configuration interaction (MRCI) nonrelativistic electronic structure calculations, and the coupling surface is obtained from lower level complete active space self-consistent field (CASSCF) calculations using the effective nuclear charge one-electron Breit-Pauli expression for the spin-orbit interaction. We find that the resulting spin-orbit splittings match the known values for O(P-3), O(D-1), and OH((II)-I-2) sufficiently accurately to be useful for dynamics calculations. Also, the electronic basis can be truncated to seven states (1 (3)A', 1 (3)A", and 1 (1)A') without seriously distorting these asymptotic splittings. We show that the seven states may be exactly decoupled into a set of four, which contains the singlet, and a set of three states from the triplets. We find that the spin-orbit matrix elements vary smoothly with geometry, so that a relatively simple function can be used to interpolate matrix elements for all geometries. The cross sections for reaction are calculated using a trajectory surface-hopping (TSH) approach in conjunction with a ''diabatic'' representation based on the nonrelativistic potentials and the CASSCF spin-orbit coupling matrix. An application of this approach is presented to the O + H-2 reaction, using the 1 (1)A' state of Dobbyn and Knowles, and 1 (3)A' and 1 (3)A" states of Walch and Kuppermann [slightly modified so that they are asymptotically degenerate in the product (H + OH) region]. The states show a singlet-triplet (S-T) crossing that is generally on the product side of the barrier on the triplet surfaces. The TSH results indicate that only a few percent of the trajectories undergo intersystem crossing (either from singlet to triplet, or vise versa) at the S-T crossing, so the effect of these transitions on measurable properties of the reaction dynamics is small. However, those trajectories that undergo triplet to singlet transition have much higher product rotational excitation than those that react on the triplet alone. We find that a much larger fraction of trajectories (20%-40%) undergo hopping between the two triplet states, and this leads to an averaging of the dynamical results for the two states.