Methane is an ubiquitous molecule, present as a minor component in many environments, including the Earth and planet atmospheres. Its van der Waals interaction with the main gases is an important ingredient for the understanding of radiative properties for those atmospheres. We present here the first precise determination of the interaction between CH4 and H2. We compute the interaction in an ab initio coupled cluster formalism, with extended atomic bases. We compare a pure CCSD(T) approach to an explicitly correlated CCSD(T)-F12a formalism. The full geometry of scattering two rigid molecules is used, resulting in a potential energy surface depending on 5 degrees of freedom. The long-range part of the ab initio computation is compared with an analytic multipolar expansion. The potential is fit onto a suitable formalism for subsequent scattering dynamics. The potential well is computed at -92.92 cm-1, an intermediate value if compared with other methane-diatomic molecule interactions.