We present ab initio embedded cluster studies on the mechanism of hydrogen exchange of methane with H-Zeolite Y. We found that inclusion of the Madelung field stabilizes the formation of a carbonium-like transition state, and consequently reduces the reaction barrier by 17-23 kJ/mol, relative to the corresponding bare cluster predictions. Using the CCSD(T)/6-31G(d,p) level of theory, including zero-point energy (similar to 10 kJ/mol) and tunneling (1.6 kJ/mol) corrections, the activation energy is predicted to be 124 +/- 5 and 137 +/- 5 kJ/mol for hydrogen exchange from two different binding sites. These predictions agree well with the experimental estimate of 122-130 kJ/mol. We also found that it is necessary to include the Madelung potential to find preferrential proton siting at site O1 versus site O4, in agreement with experimental observation.