A novel technique has been developed to build vessels for liquid xenon ionization detectors entirely out of an ultra-clean fluoropolymer. One such detector was operated inside a welded, He leak tight, all-fluoropolymer chamber. The measured energy resolution for 570 keV gamma rays is σ/E=5.1% at a drift field of 1.5 kV/cm, in line with the best values obtained for ionization only detectors run in LXe using conventional, metal vessels.