Stereochemistry plays a central role in controlling molecular recognition and interaction: the chemical and biological properties of molecules depend not only on the nature of their constituent atoms but also on how these atoms are positioned in space. Chiral specificity is consequently fundamental in chemical biology and pharmacology(1,2) and has accordingly been widely studied. Advances in scanning probe microscopies now make it possible to probe chiral phenomena at surfaces at the molecular level. These methods have been used to determine the chirality of adsorbed molecules(3-5), and to provide direct evidence for chiral discrimination in molecular interactions(6) and the spontaneous resolution of adsorbates into extended enantiomerically pure overlayers(3,7-9). Here we report scanning tunnelling microscopy studies of cysteine adsorbed to a (110) gold surface, which show that molecular pairs formed from a racemic mixture of this naturally occurring amino acid are exclusively homochiral, and that their binding to the gold surface is associated with local surface restructuring. Density-functional theory(10) calculations indicate that the chiral specificity of the dimer formation process is driven by the optimization of three bonds on each cysteine molecule. These findings thus provide a clear molecular-level illustration of the well known three-point contact model(11,12) for chiral recognition in a simple bimolecular system.