We discuss the application of a high resolution liquid xenon imaging chamber as a γ-ray telescope for medium energy astrophysics. The chamber, operated in the Time Projection Mode, will be capable to image any ionizing event occurring within its sensitive volume. Gamma-ray events with multiple Compton interactions will be identified as such, thus significantly enhancing the detection efficiency over a wide energy range. This represents the main advantage of the proposed liquid xenon instrument over more conventional double scatter Compton telescopes, in which stringent topological constraints limit considerably the acceptance. In the Compton regime, the excellent energy and position resolution of the detector, on the order of 3% FWHM at 1 MeV and of 250 pm RMS, respectively, will result in a 1a angular resolution of 0.5° - 0.3° for 7-ray energies of 1-20 MeV. The ambiguity in source location that characterizes the Compton measurement can be removed for 7-ray events of high enough energy to allow the reconstruction of the direction of the Compton electron. In the pair production regime, the incoming γ-ray direction can also be uniquely determined from the reconstructed openining angle of the electron-positron pair. An effective discrimination against charged and neutral background events is a direct consequence of the detector imaging capability. The versatility of the liquid xenon telescope and its unique characteristics will allow a large variety of γ-ray emitting sources to be explored with high sensitivity.