The rate constants for the reactions of chlorine atoms with the complete series of the three bromomethanes CH3Br (1), CH2Br2 (2), and CHBr3 (3) were measured in a very low pressure reactor, employing a microwave discharge for the generation of Cl atoms with mass spectrometric detection of reactants and products. The experiments were performed in the temperature range 273-363 K and at total pressures similar to 1 mTorr. The reactions proceed via hydrogen atom transfer leading to HCl product and the corresponding bromomethyl radicals. Their rate constant expressions are (in cm(3) molecule(-1) s(-1)): k(l) = (1.66 +/- 0.14) x 10(-11) exp(-1072 +/- 46/T), k(2) = (0.84 +/-0.15) x 10(-11) exp(-911 +/- 101/T), and k(3) = (0.43 +/- 0.11) x 10(-11) exp(-809 +/- 142/T). The activation energy of the reaction decreases with additional bromine substitution, which is attributed to the gradual weakening of the corresponding C-H bond strength. Ab initio theoretical calculations performed at the MP2/6-31++G(2d,2p) level of theory suggest C-H bond strengths for CH3Br, CH2Br2, and CHBr3 of 416.58, 407.03, and 396.60 kJ mol(-1), respectively.