Density functional theory calculations were performed to study the dissociative chemisorption of methane over Pt(111) with the idea of finding the minimum energy path for the reaction and its dependence on surface coverage. Two approaches were used to evaluate this problem; first, we used different sizes of supercells (2x2, 3x3, 4x4) in order to decrease surface coverage in the absence of pre-adsorbed H and CH3 fragments to calculate the energy barriers of dissociation. The second approach uses a 4x4 unit cell and surface coverage is simulated by adding pre-absorbed H and CH3 fragments. Results for both approaches show that in general the height of the dissociation barriers increases as the surface coverage increases, although, the first approach yields slightly lower barriers due to the fact that all repeatable images of the incident molecule are approaching the surface simultaneously. Using the reaction path formulation we were able to compute the potential energy surface for CH4 dissociation. Our results suggest that excitation of the symmetric stretch and bend modes will likely increase the probability for reaction.