An autocatalytic mechanism for helium incorporation into buckminsterfullerene has been examined by MNDO, density functional theory (DFT), and ab initio calculations. The mechanism involves dimerization of two molecules by [2+2] cycloaddition between double bonds at hexagon junctions, formation of a stable closed-shell window, and helium insertion through this window. According to MNDO, the activation barriers do not exceed 100 kcal/mol for any of these steps. At the DFT level, the window isomer is kinetically less stable and may therefore be mechanistically less relevant, Even in this case, the effective DFT activation barrier for helium incorporation into the [2+2] dimer is around 130 kcal/mol, much lower than for buckminsterfullerene itself. Vibrational and NMR spectra are predicted for the proposed window dimer to facilitate its experimental detection. The applicability of the dimer mechanism to other noble gases and to higher fullerenes is also discussed, as well as possible variants involving helium incorporation by C-60 polymers and by tethered C-60 dimers.