A six-dimensional potential energy hypersurface (PES) for two interacting rigid methane molecules was determined from high-level quantum-mechanical ab initio computations. A total of 272 points for 17 different angular orientations on the PES were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory with basis sets of aug-cc-pVTZ and aug-cc-pVQZ qualities. The calculated interaction energies were extrapolated to the complete basis set limit. An analytical site-site potential function with nine sites per methane molecule was fitted to the interaction energies. In addition, a semiempirical correction to the analytical potential function was introduced to take into account the effects of zero-point vibrations. This correction includes adjustments of the dispersion coefficients and of a single-parameter within the fit to the measured values of the second virial coefficient B(T) at room temperature. Quantitative agreement was then obtained with the measured B values over the whole temperature range of the measurements. The calculated B values should definitely be more reliable at very low temperatures (T<150 K) than values extrapolated using the currently recommended equation of state.