On the basis of semiempirical and high-level ab initio calculations, theoretical evidence is presented of a "window" mechanism operable on the surface of C60 and other fullerenes. Through this mechanism, large holes may be formed in fullerenes excited to their triplet state, openings through which atoms and small molecules can pass. This work provides a theoretical foundation for experiments that have prepared endohedral noble gas compounds of C60 under thermal excitation. A method is proposed that could increase the efficiency of the process of noble gas insertion into C60 and provide a more general means to create endohedral fullerene compounds.