Chirality has an important role in the drug design because enantiomers may exhibit different bioactivity when interacting with macromolecules of a living organism. In our previous work, based on the analysis of a set of 100 chiral drugs, a relationship was established between the sign of chirality of enantiomers and their bioactivity. To understand the reasons for the observed patterns of chiral specificity of drug enantiomers, the interaction of 10 enantiomeric pairs of chiral drugs with the corresponding target proteins has been considered using molecular docking and further postprocessing by quantum chemistry methods. The data obtained confirm that the energetic aspect of the interaction between opposite enantiomers and target protein affects the enantiomer biological activity. In addition, the results show that molecular docking is able to distinguish between bioactive and inactive/less active enantiomers, although many docking programs are not accurate enough to distinguish a weak inhibitor from a strong one.