The interaction potential of the He-CaH((2)Sigma(+)) van der Waals complex is computed with the partially spin-restricted open-shell single and double excitation coupled cluster method with perturbative triples [RCCSD(T)] for more than 3700 geometries. An accurate fit of the three-dimensional potential is made available for the RCCSD as well as the RCCSD(T) results. Also the CaH diatomic potential is calculated at the RCCSD(T) level and shown to be very accurate by comparison of computed vibrational levels and rotational constants to spectroscopic data. In the accompanying paper the potentials are employed in a study of collisions of He with CaH at cold and ultracold temperatures. (C) 2003 American Institute of Physics.