A novel chiral interferometer is proposed that allows for a direct measurement of the phase of the transmission coefficient for transport through a variety of mesoscopic structures in a strong magnetic field. The effects of electron-electron interaction on this phase are investigated with the use of finite-size bosonization techniques combined with perturbation theory resummation. New non-Fermi-liquid phenomena are predicted in the fractional quantum Hall effect regime that may be used to distinguish experimentally between Luttinger and Fermi liquids.