The formation of a Ag stabilized regular step lattice on vicinal Si(111) miscut towards [11-2] is reported. The step bunching characteristic of the clean surface is prevented by a single-domain Si(111)-(3x1)-Ag reconstruction. The nanostructured surface is used as a template for growing one-dimensional arrays of 1 nm sized Ag quantum dots with a preferential spacing of 1.5 nm along the rows.