We report an ab initio-based global potential energy surface for H+CH4 that describes the abstraction and exchange reactions. The PES, which is invariant with respect to any permutation of five H atoms, is a fit to 20,728 electronic energies calculated using the partially spin-restricted coupled-cluster method (RCCSD(T)) with a moderately large basis (aug-cc-pVTZ). A first set of quasiclassical trajectory calculations using this PES are reported for the H+CD4-->HD+CD3 reaction at collision energies of 0.65 and 1.52 eV and are compared to experiment and recent direct dynamics calculations done with density functional theory.