The Large Underground Xenon (LUX) experiment operates at the Sanford Underground Research Facility to detect nuclear recoils from the hypothetical Weakly Interacting Massive Particles (WIMPs) on a liquid xenon target. Liquid xenon typically contains trace amounts of the noble radioactive isotopes $^{85}$Kr and $^{39}$Ar that are not removed by the {\em in situ} gas purification system. The decays of these isotopes at concentrations typical of research-grade xenon would be a dominant background for a WIMP search exmperiment. To remove these impurities from the liquid xenon, a chromatographic separation system based on adsorption on activated charcoal was built. 400\,kg of xenon was processed, reducing the average concentration of krypton from 130\,ppb to 3.5\,ppt as measured by a cold-trap assisted mass spectroscopy system. A 50 kg batch spiked to 0.001 g/g of krypton was processed twice and reduced to an upper limit of 0.2 ppt.
