Long-path FTIR spectroscopy and ab initio calculations combined with conventional transition state theory were used to study the kinetics of the reactions of Cl atoms with deuterated methanes. The following experimental relative rate constants for the reaction of Cl atoms at 298 +/- 5 K and 760 +/- 5 Torr were determined: CH3D, (6.5 +/- 0.5) x 10(-14); CH2D2, (4.2 +/-0.5) x 10(-14); CHD3, (1.9 +/- 0.3) x 10(-14); CD4, (5.4 +/-0.4) x 10(-15). All experimental and theoretical rate constants are in units of cm(3) molecule(-1) s(-1) and are relative to the 1.0 x 10(-13) cm(3) molecule(-1) s(-1) rate constant for the reaction of Cl with CH4. All experimental uncertainty limits are 2 sigma. The geometries, energies, and frequencies of the reactants, products, and transition states were calculated at the level of the second-order Moller-Plesset approximation using a 6-311++G-(2d,2p) basis set. The following theoretical relative rate constants were calculated at 298 K using conventional transition state theory combined with an Eckart one-dimensional tunneling correction: CH3D, 6.8 x 10(-14); CH2D2, 4.2 x 10(-14); CHD3, 2.1 x 10(-14); CD4, 4.4 x 10(-15). The theoretical rate constants agree well with the experimental results. The curvature in both the experimental and theoretical rate constants as a function of deuteration is due to a secondary kinetic isotope effect, involving mainly the rate constant preexponential factors. The large decrease in Cl atom rate constant in going from CH4 to CH3D (i.e., the increase in curvature at CH3D) is due to the reduced symmetry in the transition state and a mass-dependent effect. The implications for previous studies, atmospheric chemistry, and chemical reactivity are discussed.