The adsorption of Xe on Pt(111) has been investigated from the arrival of the very first atoms up to completion of the monolayer using a variable-temperature Scanning Tunneling Microscope (STM). Surprisingly, in the initial stages of the adsorption Xe preferentially binds to a low coordination site, the upper edge of the platinum steps. The strong binding to these sites leads to a local repulsive interaction with further Xe atoms. Therefore, the Xe atoms located at the upper edge of the steps do not serve as nuclei for 2D Xe islands, which, instead, form on the terraces and at the lower edges of the platinum steps. Only during completion of the monolayer do these islands make contact with the atoms adsorbed at the beginning in the upper-edge positions. The full monolayer exhibits the Hexagonal Incommensurate Rotated (HIR) phase already known from earlier helium-diffraction experiments.