We have used information gained via differential cross-section experiments of the Cl + CH4 reaction in an analysis of measured thermal rate constants to determine the source of the observed non-Arrhenius behavior. Our results demonstrate that curvature in the Arrhenius plot at temperatures above room temperature can be explained by enhancement of the reaction rate when the symmetric or asymmetric stretch of CH4 is excited. At low temperatures, the apparent curvature can be explained by tunneling and modest reaction-rate enhancement by a low-frequency bending mode of CH4. An analysis of dynamical and thermal measurements of the kinetic isotope effect for Cl + CH4/CD4 indicates that tunneling enhances the reaction probability of hydrogen-atom abstraction by partially relaxing the steric restrictions for the collinear geometry of the transition state. This analysis provides an estimate of rate constants at low (atmospheric) temperatures that is higher than recommended values and provides a prediction of rate constants at high (combustion) temperatures for which measurements are not currently available. We suggest directions for future theoretical and experimental studies based on uncertainties in the current description of this important reaction.