We have applied the rotating bond umbrella (RBU) model to perform time-independent quantum scattering calculations of the O(P-3)+CH4--> OH+CH3 reaction based on a realistic analytic potential energy surface. The calculations are carried out in hypercylindrical coordinates with a log-derivative method incorporating a guided spectral transform (GST) subspace iteration technique. A single sector hyperspherical projection method is used for applying the boundary conditions. The results show that ground-state CH4 gives CH3 that is rotationally cold. For CH4 initially vibrationally excited in the C-H stretch or the H-CH3 bending mode, a bimodal CH3 rotational distribution has been observed. The product OH is a little vibrationally excited, while the umbrella mode of CH3 is moderately excited. Vibrational excitation enhances the reactivity substantially. The calculated rate constants are in good agreement with experimental measurements.