The Liquid Argon Purity Demonstrator was an R&D test stand designed to determine if electron drift lifetimes adequate for large neutrino detectors could be achieved without first evacuating the cryostat. We describe here the cryogenic system, its operations, and the apparatus used to determine the contaminant levels in the argon and to measure the electron drift lifetime. The liquid purity obtained by this system was facilitated by a gaseous argon purge. Additionally, gaseous impurities from the ullage were prevented from entering the liquid at the gas-liquid interface by condensing the gas and filtering the resulting liquid before returning to the cryostat. The measured electron drift lifetime in this test was greater than 6 ms, sustained over several periods of many weeks. Measurements of the temperature profile in the argon, to assess convective flow and boiling, were also made and are compared to simulation.