Variational transition state theory with semiclassical ground‐state transmission coefficients is applied to calculate reaction rate constants, activation energies, and kinetic isotope effects for the protium (H) and muonium (Mu) cases of H + F2 → HF + F and H + Cl2 → HCl + Cl. We examine four potential energy surfaces for H + F2 and two for H + Cl2. For H + F2 there is an unresolved difference between the available experiments; the calculations are consistent with the Mu experiments of Fleming and coworkers and with the H experiment of Albright et al. but not with the H experiment of Homann et al. For H + Cl2 the calculations based on the surface of Polanyi and coworkers are in good agreement with experiment, but those based on the surface of Last and Baer are not. For both reactions the Mu rate constants and the kinetic isotope effects are greatly enhanced by tunneling.