We demonstrate a reversible chiral switching of bis-(phthalocyaninato) terbium(III) molecules on an Ir(III) surface by low temperature scanning tunneling microscopy. With an azimuthal rotation of its upper phthalocyanine ligand, the molecule can be switched between a chiral and an achiral configuration actuated by respective inelastic electron tunneling and local current heating. Moreover, the molecular chiral configuration can be interchanged between left and right handedness during the switching manipulations, thereby opening up potential nanotechnological applications.