Quantum scattering calculations on the CH4+OH-->CH3+H2O reaction have been performed at thermal energies. The rotating bond approximation is used, treating CH3 as a pseudoatom. The OH rotation and a reactive C-H stretch of CH4 are treated explicitly as well as the bending motion and one OH local stretch vibration of H2O. Two potential energy surfaces are used. Both have accurate reactant and product rovibrational energy levels for the modes explicitly treated in the scattering calculations and incorporate the zero point energy of the other modes. They have correct bond dissociation energies and transition state geometries in reasonable accord with ab initio data. Mode selectivity is found : reactants in the ground rovibrational states produce ground state H2O, and vibrationally excited CH4 produces vibrationally excited H2O. Reactant OH rotational excitation decreases the reaction cross sections. Rate constants are obtained using an adiabatic approach to account for all degrees of freedom not explicitly treated in the scattering calculations. Large contributions due to tunneling are observed. The rate constants are in quite good agreement with previous theoretical and experimental work.