A new potential energy surface is reported for the gas-phase reaction Cl+CH4--> HCl+CH3. It is based on the analytical function of Jordan and Gilbert for the analog reaction H+CH4--> H-2+CH3, and it is calibrated by using the experimental thermal rate coefficients and kinetic isotope effects. The forward and reverse thermal rate coefficients were calculated using variational transition state theory with semiclassical transmission coefficients over a wide temperature range, 200-2500 K. This surface is also used to analyze dynamical features, such as reaction-path curvature, the coupling between the reaction coordinate and vibrational modes, and the effect of vibrational excitation on the rate coefficients. We find that excitation of C-H stretching modes and Cl-H stretching modes enhances the rate of both the forward and the reverse reactions, and excitation of the lowest frequency bending mode in the CH4 reactant also enhances the rate coefficient for the forward reaction. However, the vibrational excitation of the CH3 umbrella mode (lowest frequency mode in products) slows the reaction at temperatures below 1000 K, while above 1000 K it also accelerates the reaction.