A new analytical potential energy surface is presented for the reaction of hydrogen abstraction from methane by a hydrogen atom. It is based on an analytical expression proposed by Jordan and Gilbert [J. Chem. Phys. 102, 5669 (1995)], and its fittable parameters were obtained by a multibeginning optimization procedure to reproduce high-level ab initio electronic structure calculations obtained at the CCSD(T)/cc-pVTZ level. The ab initio information employed in the fit includes properties (equilibrium geometries, relative energies, and vibrational frequencies) of the reactants, products, saddle point, points on the reaction path, and points on the reaction swath. No experimental information is used. By comparison with the reference results we show that the resulting surface reproduces well not only the ab initio data used in the fitting but also other thermochemical and kinetic results computed at the same ab initio level, such as equilibrium constants, rate constants, and kinetic isotope effects, which were not used in the fit. In this way we show that the new potential energy surface is correctly fitted and almost as accurate as the CCSD(T)/cc-pVTZ method in describing the kinetics of the reaction. We analyze the limitations of the functional form and the fitting method employed, and suggest some solutions to their drawbacks. In a forthcoming communication, we test the quality of the new surface by comparing its results with experimental values.