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-pVQZ͒ basis set extended with a (3s3 p2d1 f 1g) 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 Ϫ1 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 Ϫ1 , excluding states observed around 25 cm Ϫ1 above the ground state. The latter states are at variance with the experimentally deduced ordering.