A new cyclic system, which is referred to as an irreversible three source chemical pump, is put forward. The cyclic system operating among three reservoirs at different chemical potentials is analogous to a heat transformer operating among three heat reservoirs. The influence of the irreversibility of finite rate mass transfer between the working fluid and the reservoirs on the cyclic performance of the chemical pump is taken into account. The optimal relation between the coefficient of performance and the rate of energy pumping is derived. The maximum rate of energy pumping and the corresponding coefficient of performance are calculated. On the basis of the optimal relation, some other optimal performances of the chemical pump are discussed. The results obtained here can not only enrich the theory of thermodynamics but also provide some new theoretical instructions for the optimal design and operation of real chemical pumps. Moreover, many important conclusions relative to chemical engines, which have been investigated in the literature, can be deduced directly from the results in this paper.