Potential energy surfaces have been determined for the A’ and A" states of the He(S-1)+CH(X(2) Pi) system. The interaction energies were computed using a Hartree-Fock singles and doubles CI treatment; convergence of the calculation with respect to both basis set and configuration set was investigated. The surfaces have been represented quantitatively by standard Legendre polynomial expansions and qualitatively by novel pairwise additive potentials. With the pairwise additive models, successful fits require that the centers of force be orbital based as opposed to the typical nucleus-based form. Comparison of the surfaces would suggest that the final fitted surfaces are accurate to a few tenths of a kcal/mol up to 5-10 kcal/mol. In the following paper, the dynamical consequences of the small differences between ah the surfaces will be assessed by quantum dynamics calculations of cross sections and their subsequent comparison to experiment.