A potential energy surface has been constructed for the CO dimer using the methods of intermolecular perturbation theory. The electrostatic and induction terms are described using distributed multipoles and distributed polarizabilities, the dispersion using anisotropic dispersion coefficients calculated by Rijks & Wormer, and the repulsion-penetration by an anisotropic exponential site-site function fitted to points calculated by nb initio intermolecular perturbation theory. The dispersion and induction are damped using Tang-Toennies damping functions. The potential has been used in diffusion Monte Carlo calculations of the ground rovibrational state, and the vibrationally averaged rotational constants agree well with experiment. The virial coefficient is also in good agreement with experiment, In order to achieve this agreement it is necessary to include C-9 and C-10 dispersion terms. The potential energy surface has two symmetry-equivalent versions of each of two low-lying minima, both of which are planar and approximately T-shaped. A third minimum, with a planar, slipped anti-parallel structure, has also been located. There are two nonplanar paths between the lowest pair of minima, with a barrier of only about 30 cm(-1), and one planar path with a slightly higher barrier. In the lowest rovibrational state there is a high probability that the system is in the neighborhood of the barriers. Consequently, the vibrationally averaged rotational constants are significantly different from the values calculated for the equilibrium geometry.