The present tunneling microscopy study reveals that the growth of silver on Pt(111) at substrate temperatures above 620 K results in the formation of a two-dimensional alloy consisting of Ag clusters dissolved in the Pt layer [THETA(Ag)<0.5 monolayer (ML)] and Pt clusters in the Ag matrix layer (0.5 ML < THETA(Ag) < 1 ML), respectively. The embedded clusters have a narrow size distribution centered around 10 angstrom. The dissolution of silver into the Pt surface layer and vice versa proceeds from the step edges and is confined to the topmost layer. The second silver layer does not dissolve into the interface, but grows layerwise on top.