A full potential energy surface (PES) is computed for a dimer consisting of rigid CO molecules. The coupled cluster single double plus perturbative triples [CCSD(T)] method is used with the augmented correlation consistent polarized valence triple zeta atomic orbital basis (aug-cc-pVTZ) with bond orbitals in the middle of the CO-CO bond. The PES is fitted in terms of analytic functions and the fitted potential is used to compute the lowest rovibrational states of the dimer. Semi-quantitative agreement with recent millimeter-wave experiments (M.D. Brookes and A.R.W. McKellar, J Chem. Phys., 1999, 1111 7321-7328; D. A. Roth, L. A. Surin, B. S. Dumesh. G. Winnewisser and I. Pak, J Chem. Phys., 2000 113 3034-3038 and J. Tang et al., J. Mol. Spectrosc., 2002, 214, 87-93) is found.