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The two-dimensional (2D) superconducting state is a fragile state of matter susceptible to quantum phase fluctuations. Although superconductivity has been observed in ultrathin metal films down to a few layers, it is still not known whether a single layer of ordered metal atoms, which represents the ultimate 2D limit of a crystalline film, could be superconducting. Here we report scanning tunnelling microscopy measurements on single atomic layers of Pb and In grown epitaxially on Si(111) substrate, and demonstrate unambiguously that superconductivity does exist at such a 2D extreme. The film shows a superconducting transition temperature of 1.83 K for an atom areal density n=10.44 Pb atoms nm−2, 1.52 K for n=9.40 Pb atoms nm−2 and 3.18 K for n=9.40 In atoms nm−2, respectively. We confirm the occurrence of superconductivity by the presence of superconducting vortices under magnetic field. In situ angle-resolved photoemission spectroscopy measurements reveal that the observed superconductivity is due to the interplay between the Pb–Pb (In–In) metallic and the Pb–Si (In–Si) covalent bondings. [ABSTRACT FROM AUTHOR]