Extrapolation from ab initio coupled Hartree-Fock calculations is used to estimate the anisotropic C-13 nuclear shielding tensor for each site in C60. The principal components of the symmetric shielding tensor are 179, 10, and -51 ppm. The derived chemical shifts have the same pattern as those deduced from solid-state NMR measurements, and their mean differs from the experimental shift by less than 4 ppm. The large diamagnetic component is associated with a near-radical local axis and the paramagnetic component with the normal to the local mirror plane.