Intermetallic compounds with the space group P213 such as PdGa, RhSi, and CoSi are promising candidates for the probing of chirality due to their exotic chemical and physical properties. Taking PdGa as an example, at least three catalogs of chirality can be found in this family of compounds as a result of their noncentrosymmetric bulk structure. a) Bulk chirality. Pd and Ga atoms are helically stacked along the [111] polar direction, suggesting the existence of two enantiomers with reversed handedness of helices. b) Surface chirality. For the threefold symmetric (111) surface of the B20 compounds, although the topmost layer of Pd atoms is achiral, the Pd and Ga trimers in the 2 nd and 3 rd outmost surface layers could induce surface chirality and then influence the surface properties of the outmost Pd layer. 17 c) Electronic structures chirality. Chiral fermions and chiral Fermi-arc surface states with reversal velocities are experimentally confirmed, which is closely related to the chirality of bulk structures. Thus, it is not surprising that B20 compounds such as PdGa have been explored a long time ago as heterogeneous catalysts. The chiral Fermi-arc surface states serve as catalytic active sites and provide stable electron baths for redox reactions. More importantly, enantioselective adsorption and elimination reaction towards prochiral molecules has been achieved on the (111) surface due to the different surface termination and the surface chirality originating from the second outmost surface layers. With these experimental facts in mind, it is interesting to ask the question of whether the bulk crystal chirality initiates the enantioselective reactions.