We have succeeded in detecting metallic transport in a monatomic layer of In on an Si(111) surface, Si(111)-sqrt[7]×sqrt[3]-In surface reconstruction, using the micro-four-point probe method. The In layer exhibited conductivity higher than the minimum metallic conductivity (the Ioffe-Regel criterion) and kept the metallic temperature dependence of resistivity down to 10 K. This is the first example of a monatomic layer, with the exception of graphene, showing metallic transport without carrier localization at cryogenic temperatures. By introducing defects on this surface, a metal-insulator transition occurred due to Anderson localization, showing hopping conduction.