The kinetic isotope effects, KIEs, for hydrogen abstraction from the isotopologs CH4, 13CH4, CH3D, and CD4 by chlorine atoms have been studied by the dual-level direct dynamics approach with the MORATE computer program. Low-level calculations of the potential energy surface were carried out at the NDDO-SRP level (in particular the AM1-SRP level), using two different sets of specific reaction parameters labeled SRP4 and SRP13. High-level structural and energetic properties of the reactants, saddle point, and products were obtained at the MP2-SAC and MP2 levels using the 6-311G(2d,d,p) basis set and were used to interpolate corrections to the low-level calculations. The dual-level calculations were carried out using the ICL-Eckart improved interpolated corrections algorithm. Tunneling was included by the microcanonical optimized multidimensional tunneling (μOMT) method, and we find that large-curvature tunneling paths usually provide the dominant contribution, with significant participation of excited vibrational states. Both rectilinear and curvilinear coordinates were applied to the unsubstituted reaction. The 12C/13C KIEs calculated at the MP2-SAC///SRP4 level using MP2 frequencies are in very close agreement with the experimental ones, with values of 1.07 and 1.06 at 243 and 297 K, respectively, as compared to experimental values of 1.07 at both temperatures. For the reaction CH3D + Cl, the calculated H/D KIEs are equal to 1.55 and 1.45 at 223 and 296 K, while the measured values are equal to 1.59 and 1.50, respectively. The H/D KIE for the reaction CD4 + Cl is calculated to decrease from 11 to 4.7 as the temperature increases from 300 K to 450 K, whereas the experimental value decreases from 12 to 3.9. We also make comparison with previous results for the unsubstituted reaction CH4 + Cl.