In order to provide a quantitative description of the relative ability of C60 to bond as an eta6 ligand, arene exchange energies for tricarbonyl(arene)chromium systems were calculated using the method of partial retention of diatomic differential overlap (PRDDO). This represents the first theoretical estimate of the relative affinity of C60 as an eta6 ligand, and results indicate that C60 is an inferior ligand compared to benzene. The arenes considered included benzene, chlorobenzene, p-difluorobenzene, and buckminsterfullerene. The exchange of benzene for C60 as an arene ligand is calculated to require 19 kcal/mol, but this can be reduced by modifying the exchanging ligand. Reduced overlap from C60 hybrid orbitals is found to be partly responsible for less favorable eta6 bonding, which suggests that larger metals such as tungsten may be better able to bond in an eta6 fashion to C60.