Potential energy surfaces for the reactions of CH4+ with H-2, HD, and D-2 have been calculated using high-level ab initio methods, including coupled cluster theory, complete active space self-consistent field, and multireference configuration interaction. The energies are extrapolated to the complete basis set limit using the basis sets aug-cc-pVXZ (X = D, T, Q, 5, 6). The CH4+ + H-2 reaction produces CH5+ and H exclusively. Three types of reaction mechanisms have been found, namely, complex-forming abstraction, scrambling, and S(N)2 displacement. The abstraction occurs via a very minor barrier and it is dominant. The other two mechanisms are negligible because of the significant barriers involved. Quantum phase space theory and variational transition state theory are used to calculate the rate coefficients as a function of temperatures in the range of 5-1000 K. The theoretical rate coefficients are compared with the available experimental data and the discrepancy is discussed. The significance of isotope effect, tunneling effect, and nuclear spin effect is investigated. The title reaction is predicted to be slightly exothermic with Delta H-r = -12.7 +/- 5.2 kJ/mol at 0 K.