Density Functional Theory calculations have been used to predict the structures of dense glycine and alanine adlayers on Cu(3,1,17)(S). Facets of this chiral Cu surface result from adsorbate-induced surface reconstruction when glycine or alanine are adsorbed and annealed on Cu(100). We have calculated the surface energy changes associated with this surface reconstruction. Our results allow the enantiospecificity of this reconstruction following adsorption of enantiopure or racemic alanine on Cu(100) to be discussed. The overall stability of glycine and alanine adlayers on Cu(3,1,17)(S) arises from an interplay between the formation of chemical bonds with the Cu surface, deformations in the adsorbed molecules during adsorption, and intermolecular hydrogen bonds within the adlayer; none of these factors individually dominates.