Corannulene (COR) buckybowls were proposed as near ideal hosts for fullerene C-60, but direct complexation of C-60 and COR has remained a challenge in supramolecular chemistry. We report the formation of surface-supported COR-.C-60 host-guest complexes by deposition of C-60 onto a COR lattice on Cu(110). Variable-temperature scanning tunneling microscopy studies reveal two distinctly different states of C-60 on the COR host lattice, with different binding energies and bowl-ball separations. The transition from a weakly bound precursor state to a strongly bound host-guest complex is found to be thermally activated. Simple model calculations show that this bistability originates from a subtle interplay between homo- and heteromolecular interactions.