Transport properties for collisions of the oxygen molecule with hydrogen atoms are computed by means of quantum scattering calculations. Because two potential energy surfaces (PESs) arise from the interaction of H(S-2) with O-2(X-3 Sigma(+)(g)), namely (2)A" and (4)A", collision integrals were computed using both PESs and then averaged with weighting by their respective spin multiplicities. A PES for the (4)A" state was computed for the interaction of O-2, frozen at its equilibrium internuclear separation, with a hydrogen atom, using a coupled-cluster method that includes all single and double excitations as well as perturbative contributions of connected triple excitation. A PES of similar quality was taken from Klos et al. [J. Chem. Phys.2008, 129, 064306] for the (2)A" state. Because the (2)A" state correlates with the deep HO2((X) over tilde (2)A") well, statistical capture boundary conditions [Rackham et al., J. Chem. Phys.2003, 119, 12895] were applied to compute the S matrix, and then the transport properties, for this state.