We report on the first observation of superconductivity in a double atomic layer of Tl on Si(1 1 1) using in situ electrical resistivity measurements in ultrahigh vacuum. The structure of the Tl bilayer was characterized by a set of techniques, including scanning tunneling microscopy, electron diffraction and photoemission spectroscopy, which confirmed the metastability and metallic nature of the Tl bilayer. The epitaxial growth of atomically thin 'soft' metallic film over the entire surface of substrate enabled us to find a macroscopic superconducting transition at 0.96 K, accompanied by thermal and quantum fluctuations of order parameter. The system also demonstrates a perpendicular-magnetic-field-induced superconductor-insulator transition, together with an intermediate metallic state. We have found that the magnetoresitivity at the lowest temperature is consistent with the Bose metal picture, which is a consequence of strong quantum fluctuations.