Horseradish peroxidase exhibits a meager stereoselectivity (E) in the sulfoxidation of thioanisole (1a) in 99.8% (v/v) methanol. The E value, however, is greatly enhanced when the enzyme forms a complex with benzohydroxamic acid (2a). These findings are rationalized by means of molecular dynamics simulations and energy minimization which correctly explain (i) why the free enzyme is not stereoselective, (ii) why 2a inhibits peroxidase-catalyzed sulfoxidation of 1a but the enzymatic formation of one enantiomer of the sulfoxide product is inhibited much more than that of the other, thereby raising peroxidase's E, and (iii) why in the presence of 2a the enzyme favors production of the S sulfoxide of 1a. The generality of the observed ligand-induced stereoselectivity enhancement is demonstrated with other hydrophobic hydroxamic acids, as well as with additional thioether substrates.