A new aspect of chiral discrimination is described. The rate of resonance transfer between chiral molecules at all separation distances is calculated using molecular quantum electrodynamics. The leading correction to the familiar electric dipole transfer rate is shown to be discriminatory, and is proportional to the optical rotatory strengths. In the near zone the rate and the discrimination in the rates for transfer to the two chiral enantiomers are proportional, to the inverse sixth power of the separation; in the far zone to the inverse square. Results are discussed for transfer between identical and nonidentical molecules. In the latter the discrimination between the two enantiomers of the molecule excited by transfer depends on the handedness of the initially excited molecule, a property that might be exploited in practical applications.