Due to its intrinsic physical properties, high density and atomic number, fast scintillation, high scintillation light yield and low ionization potential, liquid xenon is an excellent medium for the tracking and the accurate energy measurement of γ-rays in the MeV energy domain. The use of liquid xenon associated to a micro gap structure device[1] to measure 511 keV γ-rays in PET system is under investigation at Subatech. A Geant3 simulation of a full PET design made of lXe-TPC modules has been developed and the first estimations of the performances from a realistic detector are very promising: good overall sensitivity to 511 keV γ's (~ 93% for a 9 cm lXe module), good three-dimensional spatial resolution (250 µm FWHM, for first interaction vertex localization). The measurement of the 3 coordinates of the interaction vertices and the energy loss associated allow to reconstruct the correct Compton sequence of correlated annihilation γ-rays. Hence the capability to identify the first interaction vertex leads to major progresses in PET imaging: a parallax free PET tomograph with high detection sensitivity and spatial resolution. Moreover, such lXe-PET camera have an excellent rejection power on scattered events in 3D reconstruction mode.