Comparison of state-to-state differential cross sections for methane in the ground vibrational state to methane with one quantum of asymmetric stretch excitation probes the effect of C-H stretch excitation on the reaction of atomic chlorine with methane. We previously reported state-to-state differential cross sections and HCl product state population distributions for the vibrationally excited reaction. Here we report analogous measurements of the reaction for methane in the vibrational ground state. Photolysis of molecular chlorine produces chlorine atoms that react with methane molecules at 0.16 eV collision energy. Calibrated resonance-enhanced multiphoton ionization (REMPI) determines the product state distributions, and the core-extraction technique measures the angular scattering distribution. The product HCl(v=0) is formed with a cold rotational-state distribution and is strongly back scattered. The product state and angular scattering distributions for the ground-state reaction are consistent with a line-of-centers model in which the cone of acceptance is only narrowly open. The rotational-state distributions and comparisons to thermal rate data indicate that the C-H-Cl angle must be constrained in the transition-state region. One quantum of C-H asymmetric stretch vibrational excitation enhances the rate of reaction at a collision energy of 0.16 eV by a factor of 30 +/- 15 (+/-2 sigma). The behavior of the ground-state reaction is in marked contrast to our earlier results for the reaction of chlorine atoms with C-H stretch-excited methane, for which the state-to-state angular scattering distributions were consistent with a widely open cone of acceptance. By using the approximation that hard-sphere scattering describes the relation between impact parameter and scattering angle, we can transform the measured state-to-state differential cross section into the distribution of impact parameters that lead to reaction, which forms what we call a b map. This b map pictorially shows that the ground-state reaction occurs only for head-on collisions (with small impact parameters), whereas C-H stretch vibrational excitation allows reactivity to spread to the periphery of the methane molecule. The data indicate that the mechanism of vibrational enhancement is opening of the cone of acceptance and lessening the necessity for collinearity of the C-H-Cl angle in the transition-state region.