Histidine phosphatases are a class of enzymes that are characterized by the presence of a conserved RHGXRXP motif. This motif contains a catalytic histidine that is being phosphorylated in the course of a dephosphorylation reaction catalyzed by these enzymes. Prostatic acid phosphatase (PAP) is one such enzyme. The dephosphorylation of phosphotyrosine by PAP is a two-step process. The first step involves the transfer of a phosphate group from the substrate to the histidine (His-12). The present study reports on the details of the first step of this reaction, which was investigated using a series of quantum chemistry calculations. A number of quantum models were constructed containing various residues that were thought to play a role in the mechanism. In all these models, the transition state displayed an associative character. The transition state is stabilized by three active site arginines (Argt 1, Arg15, and Arg79), two of which belong to the aforementioned conserved motif. The work also demonstrated that His12 could act as a nucleophile. The enzyme is further characterized by a His257-Asp258 motif. The role of Asp258 has been elusive. In this work, we propose that Asp258 acts as a proton donor which becomes protonated when the substrate enters the binding pocket. Evidence is also obtained that the transfer of a proton from Asp258 to the leaving group is possibly mediated by a water molecule in the active site. The work also underlines the importance of His257 in lowering the energy barrier for the nucleophilic attack.