The O+ H 2→ OH+ H reaction is considered to be the key step in initiating oxygen chemistry in shocked interstellar molecular clouds. We present extensive quantum scattering calculations of rate coefficients of the O+ H 2→ OH+ H reaction involving both ortho and para hydrogen in the temperature range 100-4000 K. The role of vibrational excitation of H 2 is examined, and it is shown that vibrational excitation of the molecule has a significant effect on reactivity, especially at low temperatures. At 100 K, the rate coefficient increases by about 11 orders of magnitude when the H 2 vibrational quantum number is increased from v= 0 to v= 3. Initial vibrational state selected cross sections, rate coefficients, and product OH vibrational level distributions are presented for v= 0-3 of the H 2 molecule.