Accurate intermolecular potentials between hydrocarbons and water are essential for the prediction of properties of systems containing these components. Unfortunately, current experimental techniques are unable to measure directly the interaction potential between methane and water molecules. Therefore we have used quantum mechanical calculations, both ab initio and density functional theory (DFT) calculations, in order to determine the H2O-CH4 potential energy surface (PES) accurately for use in modeling gas hydrates. Ab initio methods were found to be more accurate than DFT methods, which do not account for the substantial dispersion interactions that exist between methane and water. Electron correlation was found to be treated accurately by MP2. However, a large basis set, cc-pVQZ was found to be necessary to compute the binding energies to within 0.1 kcal/mol of the basis set limit. In order to sample accurately the PES, the H2O-CH4 binding energy was computed at 18 000 points. For these computations to be feasible, a new method was developed in which all 18 000 points were computed using MP2/6-31++G(2d,2p) and then corrected to near the accuracy of MP2/cc-pVQZ. The PES calculated from the six-dimensional numerical potential agrees very well with far infrared vibration-rotation-tunneling spectroscopic data and experimental second virial coefficient data at the potential minimum and larger separations. The exp-6 potential proves to be the best representation of the H2O-CH4 interaction.