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We report high transition temperature superconductivity in one unit-cell (UC) thick FeSe films grown on a Se-etched SrTiO 3 (001) substrate by molecular beam epitaxy (MBE). A superconducting gap as large as 20 meV and the magnetic field induced vortex state revealed by in situ scanning tunneling microscopy (STM) suggest that the superconductivity of the 1 UC FeSe films could occur around 77 K. The control transport measurement shows that the onset superconductivity temperature is well above 50 K. Our work not only demonstrates a powerful way for finding new superconductors and for raising T C, but also provides a well-defined platform for systematic studies of the mechanism of unconventional superconductivity by using different superconducting materials and substrates.