The overall rate constant for H + CH3SH has been studied over 296-1007 K in an Ar bath gas using the laser flash photolysis method at 193 nm. H atoms were generated from CH3SH and in some cases NH3, They were detected via time-resolved resonance fluorescence. The results are summarized as k = (3.45 +/- 0.19) X 10(-11) cm(3) molecule(-1) s(-1) exp (-6.92 +/- 0.16 kJ mol(-1)/RT) where the errors in the Arrhenius parameters are the statistical uncertainties, at the 2 sigma level. Overall error limits of 9% for k are proposed. In the overlapping temperature range there is very good agreement with the resonance fluorescence measurements of Wine et al Ab initio data and transition state theory yield moderate accord with the total rate constant, but not with prior mass spectrometry measurements of the main product channels leading to CH3S + H-2 and CH3 + H2S by Amano et al.