We report a high-quality, ab initio, full-dimensional global potential energy surface (PES) for the Cl((2)P, (2)P(3/2)) + CH(4) reaction, which describes both the abstraction (HCl + CH(3)) and substitution (H + CH(3)Cl) channels. The analytical PES is a least-squares fit, using a basis of permutationally invariant polynomials, to roughly 16,000 ab initio energy points, obtained by an efficient composite method, including counterpoise and spin-orbit corrections for the entrance channel. This composite method is shown to provide accuracy almost equal to all-electron CCSD(T)/aug-cc-pCVQZ results, but at much lower computational cost. Details of the PES, as well as additional high-level benchmark characterization of structures and energetics are reported. The PES has classical barrier heights of 2650 and 15,060 cm(-1) (relative to Cl((2)P(3/2)) + CH(4)(eq)), respectively, for the abstraction and substitution reactions, in good agreement with the corresponding new computed benchmark values, 2670 and 14,720 cm(-1). The PES also accurately describes the potential wells in the entrance and exit channels for the abstraction reaction. Quasiclassical trajectory calculations using the PES show that (a) the inclusion of the spin-orbit corrections in the PES decreases the cross sections by a factor of 1.5-2.5 at low collision energies (E(coll)); (b) at E(coll) ≈ 13,000 cm(-1) the substitution channel opens and the H/HCl ratio increases rapidly with E(coll); (c) the maximum impact parameter (b(max)) for the abstraction reaction is ~6 bohr; whereas b(max) is only ~2 bohr for the substitution; (d) the HCl and CH(3) products are mainly in the vibrational ground state even at very high E(coll); and (e) the HCl rotational distributions are cold, in excellent agreement with experiment at E(coll) = 1280 cm(-1).