The reaction between atomic oxygen and molecular hydrogen is an important one in astrochemistry as it regulates the abundance of the hydroxyl radical and serves to open the chemistry of oxygen in diverse astronomical environments. However, the existence of a high activation barrier in the reaction with ground state oxygen atoms limits its efficiency in cold gas. In this study we calculate the dependence of the reaction rate coefficient on the rotational and vibrational state of H_2_ and evaluate the impact on the abundance of OH in interstellar regions strongly irradiated by far-UV photons, where H_2_ can be efficiently pumped to excited vibrational states. We use a recently calculated potential energy surface and carry out time-independent quantum mechanical scattering calculations to compute rate coefficients for the reaction O(^3^P)+H_2_(v,j)-->OH+H, with H_2_ in vibrational states v=0-7 and rotational states j=0-10. We find that the reaction becomes significantly faster with increasing vibrational quantum number of H_2_, although even for high vibrational states of H_2_ (v=4-5) for which the reaction is barrierless, the rate coefficient does not strictly attain the collision limit and still maintains a positive dependence with temperature. We implemented the calculated state-specific rate coefficients in the Meudon PDR code to model the Orion Bar PDR and evaluate the impact on the abundance of the OH radical. We find the fractional abundance of OH is enhanced by up to one order of magnitude in regions of the cloud corresponding to AV=1.3-2.3, compared to the use of a thermal rate coefficient for O+H_2_, although the impact on the column density of OH is modest, of about 60%. The calculated rate coefficients will be useful to model and interpret JWST observations of OH in strongly UV-illuminated environments.