The development of a new method for epitaxial growth of metals in solution is discussed and illustrated by proof-of-concept results. Cyclic voltammetry and scanning tunneling microscopy are employed to carry out and monitor a quasi-perfect, two-dimensional growth of up to 35 layers of Ag on Au(111) by repetitive galvanic displacement of an underpotentially deposited (UPD) Pb monolayer. The excellent quality of the deposit is manifested by an unchanged Pb UPD voltammetry and ascertained by a flat and uniform surface morphology maintained during the entire growth process. An X-ray photoelectron spectroscopy analysis finds no traces of Pb in the Ag deposit.