It has long been thought that ferroelectricity would vanish in a ferroelectric flm under a critical thickness,partly because the incompletely screened depolarization feld in ultrathin flm raises the total energy of the system.First principle studies on perovskite ferroelectrics in the last twenty years claim that the critical thickness,if exists,is no more than several unit cells in both stress-free and epitaxial growth regimes.The experiments performed on the epitaxially grown perovskite compounds reveal that the out-of-plane polarization persists down to several unit cells.The thinnest ferroelectric perovskite flm is the epitaxial PbTiO3 grown on insulating SrTiO3 substrate,which shows very fne domain structure on a flm as thin as three unit cells.It is further pointed out theoretically that the compressive strain will suppress the in-plane polarization and support the out-of-plane one in the epitaxially grown perovskite flms; if there is no strain,the in-plane polarization can persist down to one unit cell with the out-of plane polarization suppressed.Here we report the ferroelectricity in single unit cell SnTe flm with in-plane spontaneous polarization.In the bulk form,the binary compound SnTe is one of the simplest ferroelectrics given that ferroelectricity needs at least two elements acting as cations and anions.Nearly free-standing SnTe thin flm was grown on graphitized 6H-SiC(0001).Scanning tunneling spectroscopy reveals the band bending at the edge of an island.Various domain structures are observed.Spinpolarized electron valleys are induced by the polarization.