Abstract: The measurement of the time of flight of the two 511 keV gammas recorded in coincidence in a PET scanner provides an effective way of reducing the random background and therefore increases the scanner sensitivity, provided that the coincidence resolving time (CRT) of the gammas is sufficiently good. The best commercial PET-TOF system today (based in LYSO crystals and digital SiPMs), is the VEREOS of Philips, boasting a CRT of 316 ps (FWHM). In this paper we present a Monte Carlo investigation of the CRT performance of a PET scanner exploiting the scintillating properties of liquid xenon. We find that an excellent CRT of 70 ps (depending on the PDE of the sensor) can be obtained if the scanner is instrumented with silicon photomultipliers (SiPMs) sensitive to the ultraviolet light emitted by xenon. Alternatively, a CRT of 160 ps can be obtained instrumenting the scanner with (much cheaper) blue-sensitive SiPMs coated with a suitable wavelength shifter. These results show the excellent time of flight capabilities of a PET device based in liquid xenon.