Calculations were carried out for 25 isotopologues of the title reaction for various combinations of Cl-35, Cl-37, C-12, C-13, H, and D. The computed rate constants are based on harmonic vibrational frequencies calculated at the CCSD(T)/aug-cc-pVTZ level of theory and X-ij vibrational anharmonicity coefficients calculated at the CCSD(T) /aug-cc-pVDZ level of theory. For some reactions, anharmonicity coefficients were also computed at the CCSD(T)/aug-cc-pVTZ level of theory. The classical reaction barrier was taken from Eskola et al. [J. Phys. Chem. A 2008, 112, 7391-7401], who extrapolated CCSD(T) calculations to the complete basis set limit. Rate constants were calculated for temperatures from similar to 100 to similar to 2000 K. The computed ab initio rate constant for the normal isotopologue is in good agreement with experiments over the entire temperature range (similar to 10% lower than the recommended experimental value at 298 K). The ab initio H/D kinetic isotope effects (KIEs) for CH3D, CH2D2, CHD3, and CD4 are in very good agreement with literature experimental data. The ab initio C-12/C-13 KIE is in error by similar to 2% at 298 K for calculations using X-ij coefficients computed with the aug-cc-pVDZ basis set, but the error is reduced to similar to 1% when X-ij coefficients computed with the larger aug-cc-pVTZ basis set are used. Systematic improvements appear to be possible. The present SCTST results are found to be more accurate than those from other theoretical calculations. Overall, this is a very promising method for computing ab initio kinetic isotope effects.