A procedure based on the reproducing kernel Hilbert space (RKHS) interpolation method has been implemented to produce a globally smooth potential energy surface (PES) for the 1 A(') state of the S(D-1)+H-2 reaction from a set of accurate ab initio data, calculated at the multireference configuration interaction level with augmented polarized quadruple-zeta basis sets and arranged on a three-dimensional regular full grid in the Jacobi coordinates. The procedure includes removing a small number of questionable ab initio data points, implementing a recently developed technique for efficiently handling a partially filled grid, and adopting a sequence of regularizations for attaining additional smoothness. The resulting RKHS PES is analytic, first-order differentiable, and fast to evaluate. Quasiclassical trajectory calculations have been performed and compared with the results based on a recent hybrid PES obtained from a combination of the RKHS interpolation in the entrance channel and Murrell-Carter (MC)-type fitting in the exit channel from the same set of ab initio data. Comparisons with recent experimental measurements show improvement of the present RKHS PES over the existing hybrid RKHS-MC PES. The results demonstrate that the entrance channel Jacobi coordinates can still be a good candidate in sampling the full configuration space for reactive systems involving three atoms.