A process for making high purity argon is disclosed in which crude argon containing less than about 0.8 mol % oxygen is recovered from air in a cryogenic distillation system, the crude argon is purified by removing oxygen in a getter system, and other impurities are removed by cryogenic distillation to yield a high purity argon product. The crude argon purification system is heat integrated with the main cryogenic air separation system. High purity argon can be produced at argon recoveries greater than 90% by utilizing structured packing in at least a portion of the argon sidearm column.