The trapping of single molecules on surfaces without the formation of strong covalent bonds is a prerequisite for molecular recognition and the exploitation of molecular function. On nanopatterned surfaces, molecules may be selectively trapped and addressed. In a boron nitride nanomesh formed on Rh(111), the pattern consisted of holes 2 nanometers in diameter on a hexagonal superlattice, separated by about 3 nanometers. The trapping was further investigated with density functional theory and the photoemission of adsorbed xenon, where the holes were identified as regions of low work function. The analysis showed that the trapping potential was localized at the rims of the holes.