Neutrino oscillation experiments have shown de nite evidence for non-zero neutrino masses. However, these experiments only tell us about neutrino mass di erences, and nothing about the absolute masses themselves. The observation of neutrinoless double-beta (0 ) decay, a hypothetical nuclear transition, would provide the rst absolute mass scale measurement of the neutrino outside of cosmology. This decay would imply the neutrino to be a Majorana particle, the rst fermion of its kind. 0 decay would also be the rst observation of lepton number violation. The Enriched Xenon Observatory (EXO) is currently searching for 0 decay in 136Xe with a half-life greater than 1025 years. EXO-200 is the rst experiment of the EXO physics program, which has observed twoneutrino double beta decay (2 ) in 136Xe for the rst time, with a half-life of 2:165 0:075 1021 years [1]. This is the longest measured half-life to date. EXO is now designing a 5-tonne scale detector, nEXO, to be sensitive to the inverted-scale hierarchy. Despite the careful selection of radiopure substances for the detector, the existence of trace levels of 222Rn is inevitable. One of the daughters of 222Rn, 214Bi, can emit photons at the Q-value for 0 decay, making it a critical background. This dissertation investigates the method of Rn removal from gaseous Xe through the use of a Cu wool trap.