Many high Miller index metal surfaces are naturally chiral and exhibit enantiospecific properties when chiral molecules are adsorbed on them. The structure of real metal surfaces typically deviates from those of perfect Miller index surfaces due to thermally induced surface roughening. Here, the effect of thermal surface roughening on the enantiospecific adsorption of (R/S)-trans-1,2-dimethylcyclopropane and (RI S)-trans-1,2-dimethylcyclohexane on a series of chiral Pt surfaces vicinal to (111) is studied using atomistic and lattice models. Adsorption is probed in the dilute coverage limit and at higher coverages. The effect of thermal roughening is to diminish the differences between different Miller index surfaces with respect to their enantiospecificity. This implies that a chiral adsorbate that is not enantiodiscriminated on one surface vicinal to (111) with wide terraces is not likely to be enantiodiscriminated on any wide terrace surface vicinal to (111). Thus, the range of surfaces that are available for enantiospecific adsorption is not as large as the set of ideal Miller index surfaces would indicate.