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 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 experiment. 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.