The adsorption of cysteine onto the intrinsically chiral gold surface, Au(321)(R,S), was investigated by means of a periodic supercell density functional theory approach. The results are compared to those obtained at the same level of theory with a nonchiral surface having the same terrace orientation, the Au(111) surface. Neutral and zwitterionic cysteine forms of the L and D enantiomers are considered, as are surface coverage effects. It was found that at high coverage the zwitterionic forms of L- and D-cysteine are more stable on the Au(321)(R,S) faces of the stepped surface and also on the flat Au(111) surface, leading to highly organized cysteine monolayers. However, at low coverage the adsorption of cysteine dimers, with the pairs interacting through their carbonyl groups, is more favorable than or at least equally favorable to the adsorption of single cysteine molecules on both surfaces. A comparison between the cysteine adsorption on the two different surface structures shows that the adsorption on the stepped surface is clearly more favorable than on the flat surface, revealing the importance of the low-coordinated gold atoms in the adsorption of these species. Furthermore, non-negligible differences between the adsorption energy of the enantiomers of cysteine were found both at high and low coverage, thus showing the enantiospecificity of this intrinsically chiral surface regarding cysteine adsorption. This adsorption occurs with the cysteine binding the surface through only one contact point (by its sulfur atom), in contrast to previous work where the enantiospecific adsorption of cysteine has been related to two nonequivalent binding sites of the cysteine enantiomers with the surface.