A laser flash photolysis-resonance fluorescence technique has been employed to determine absolute rate coefficients for the CH3F + Cl reaction in N-2 bath gas in the temperature range of 200-700 K and pressure range of 33-133 hPa. The data were fitted to a modified Arrhenius expression k(T) = 1.14 x 10(-12) x (T/298)(2.26) exp{-313/T}. The OH and Cl reaction rates of (CH3F)-C-13 and CD3F have been measured by long-path FTIR spectroscopy relative to CH3F at 298 +/- 2 K and 1013 +/- 10 hPa in purified air. The FTIR spectra were fitted using a nonlinear least-squares spectral fitting method including line data from the HITRAN database and measured infrared spectra as references. The relative reaction rates defined by alpha = k(light)/k(heavy) were determined to be k(OH+CH3F)/k(OH+CD3F) = 4.067 +/- 0.018, k(OH+CH3F)/k(OH+13CH3F) = 1.067 +/- 0.006, k(Cl+CH3F)/k(Cl+CD3F) = 5.11 +/- 0.07, and k(Cl+CH3F)/k(Cl+13CH3F) = 1.016 +/- 0.006. The carbon-13 and deuterium kinetic isotope effects in the OH and Cl reactions of CH3F have been further investigated by quantum chemistry methods and variational transition state theory.