Diffusion Monte Carlo (DMC) calculations of the intermolecular vibrational ground states of CO(He)(n) clusters with n=1-12, for CO v=0 are reported. The intermolecular degrees of freedom of the clusters are treated in full dimensionality and a pairwise additive potential surface is used in which the He-CO interaction is described by a recently developed scheme which combines density functional theory (DFT) with the long-range dispersion contributions obtained from a perturbative theory. The calculations yield intermolecular ground-state energies, He density distributions, radial and angular density probability distributions. Optimal structures by SIMPLEX minimization have been calculated to estimate zero-point energy (ZPE) and quantum effects.