The reactions of Cl atoms with methane and three chlorinated methanes (CH3Cl, CH2Cl2, and CHCl3) have been studied experimentally using the discharge flow/resonance fluorescence technique over wide ranges of temperature and at pressures between 1.4 and 8.8 Torr. The rate constants were obtained in direct experiments as functions of temperature: k(1)(Cl + CH4) = 1.30 x 10(-19)T 2.69 exp(-497 K/T) (295-1104 K), k(2)(Cl + CH3Cl) = 4.00 x 10(-14)T(0.92) exp(-795 K/T) (300-843 K), k(3)(Cl + CH2Cl2) = 1.48 X 10(-16)T(1.58) exp(-360 K/T) (296-7.90 K), and k(4)(Cl + CHCl3) = 1-19 X 10(-16)T(1.51) exp(-571 K/T) (297-854 K) cm(3) molecule(-1) s(-1). Results of earlier experimental and theoretical studies of the reactions of Cl atoms with methane and chloromethanes are analyzed and compared with the results of the current investigation. It is demonstrated that the existing theoretical models of reactions 2-4 are in disagreement with the experiments and thus are not suitable for use in extrapolating the experimental results to conditions outside the experimental ranges. Thus, no better alternative to the use of experimental modified Arrhenius fits can be proposed at this time. A transition-state theory model of reaction I (Cl + CH4) was created on the basis of ab initio calculations and analysis of the experimental data and was used to extrapolate the latter to temperatures outside the experimental ranges. The model results in the expression k(1)(Cl + CH4) = 5.26 x 10(-19) T-2.49 exp(-589 K/T) cm(3) molecule(-1) s(-1) (200-3000 K) for the. temperature dependence of the rate constant. Temperature dependences of the rate constants of the reverse R + HCl --> Cl + RH reactions were derived on the basis of the experimental data, modeling, and thermochemical information.