The first three-dimensional ab initio intermolecular potential energy surface of the Ar-CO van der Waals complex is calculated using the coupled cluster singles and doubles including connected triples model and the augmented correlation-consistent polarized valence quadruple zeta (aug-cc-pVQZ) basis set extended with a (3s3p2d1f1g) set of midbond functions. The three-dimensional surface is averaged over the three lowest vibrational states of CO. Rovibrational energies are calculated up to 50 cm(-1) above the ground state, thus enabling comprehensive comparison between theory and available experimental data as well as providing detailed guidance for future spectroscopic investigations of higher-lying states. The experimental transitions are reproduced with a root-mean-square error of 0.13 cm-1, excluding states observed around 25 cm(-1) above the ground state. The latter states are at variance with the experimentally deduced ordering.