We identify the formation of bound 129Xe-Xe molecules as the primary fundamental spin-relaxation process at densities below 14 amagat. Low pressure Xe relaxation rate measurements as a function of gas composition show that Xe-Xe molecular relaxation contributes 1/T1 = 1/4.1 h to the total observed relaxation rate. The measured rate is consistent with theoretical estimates deduced from previously measured NMR chemical shifts. At atmospheric pressure the molecular relaxation is more than an order of magnitude stronger than binary relaxation. Confusion of molecular and wall relaxation mechanisms has historically caused wall relaxation rates to be overestimated.