A process for producing high purity hydrogen is disclosed. Specifically, the process includes (1) partially oxidizing a refinery offgas feedstock to produce a synthesis gas mixture of carbon monoxide and hydrogen, (2) reacting the synthesis gas mixture with steam to convert the carbon monoxide into a raw gas mixture which primarily includes carbon dioxide and hydrogen, and (3) purifying the raw gas mixture to produce high purity hydrogen and a reject gas mixture of impurities. In a preferred embodiment, the purification step occurs in a pressure swing adsorption unit.Alternative embodiments are also described, each of which essentially involve the optional treatment and/or use of the reject gas mixture of impurities.