The potential energy surface for the ground state of He-H-2(+) is calculated using ab initio QCISD(T) calculations and a correlation-consistent basis set. The geometries chosen include all combinations of 21 intermolecular distances R, three H-H distances r, and seven Jacobi angles theta. The final potential is fitted to a functional form that incorporates the correct long-range behavior. Close-coupling calculations of both low-lying and near-dissociation vibration-rotation states are carried out. The results are expected to be of assistance in assigning the microwave spectra of He-H-2(+) in near-dissociation states [Carrington et al., Chem. Phys. Lett. 260, 395 (1996)].