The rotational dynamics of C60 in the solid state have been investigated with carbon-13 nuclear magnetic resonance (13C NMR). The relaxation rate due to chemical shift anisotropy (1/9T1CSA1) was precisely measured from the magnetic field dependence of T1, allowing the molecular reorientational correlation time, τ, to be determined. At 283 kelvin, τ = 9.1 picoseconds; with the assumption of diffusional reorientation this implies a rotational diffusion constant D = 1.8 x 1010 per second. This reorientation time is only three times as long as the calculated τ for free rotation and is shorter than the value measured for C60 in solution (15.5 picoseconds). Below 260 kelvin a second phase with a much longer reorientation time was observed, consistent with recent reports of an orientational phase transition in solid C60. In both phases τ showed Arrhenius behavior, with apparent activation energies of 1.4 and 4.2 kilocalories per mole for the high-temperature (rotator) and low-temperature (ratchet) phases, respectively. The results parallel those found for adamantane.