We have computed barrier heights of 71.8 +/- 2.0 and 216.4 +/- 2.0 U mol(-1) for the reactions CH4 + CH3 center dot -> CH3 center dot + CH4 and CH4 + CH3 center dot -> H-center dot + C2H6, respectively, using explicitly correlated coupled cluster theory with singles and doubles combined with standard coupled cluster theory with up to connected quadruple excitations. Transition-state theory has been used to compute the respective reaction rate constants in the temperature interval of 250-1500 K. The computed rates for the reaction to ethane are orders of magnitude slower than those used in the mechanism of Norinaga and Deutschmann (Ind. Eng. Chem. Res. 2007, 46, 3547.) for the modeling of the chemical vapor deposition of pyrolytic carbon.