Density functional theory is used to describe the reaction profile for methane dissociation on Ga-exchanged ZSM-5. Stable structures an the reaction pathway are characterized as weakly adsorbed methane molecule and the C-H dissociation product. The transition state is also explicitly defined and optimized. The nonlocal density functional approximation is invoked to calculate the energy parameters of the reaction. The activation barrier is estimated at about 120 kJ/mol, in excellent agreement with other similar reactions. From vibrational analysis the reaction coordinate is deduced and transformation of a methane molecule on adsorption is discussed.