Adsorption of chiral molecules on chiral surfaces implies diastereomerism, evident in the adoption of distinct adsorption geometries. We show here that this diastereomerism produces a signature in the motion of chiral molecules desorbing from a chiral surface. The rotations of S- and R-alanine molecules are analyzed upon desorption from R-Cu{531} using first-principles molecular dynamics simulations. S-Ala molecules exhibit a larger angular momentum, with a clear preference for one rotational sense, whereas no such preference is observed for R-Ala molecules upon desorption from this surface. These trends would be reversed for desorption from the S-Cu{531} surface. Possible applications include chiral separation techniques and enantiospecific sensors.