The thermally induced diffusion of atomic species in noble gas matrices was studied extensively in the 1990s to investigate low-temperature solid-state reactions and to synthesize reactive intermediates. In contrast, much less is known about the diffusion of atomic species in quantum solids such as solid parahydrogen (p-H2). While hydrogen atoms were shown to diffuse in normal-hydrogen solids at 4.2 K as early as 1989, the diffusion of other atomic species in solid p-H2 has not been reported in the literature. The in situ photogeneration of atomic oxygen, by ArF laser irradiation of an O2-doped p-H2 solid at 193 nm, is studied here to investigate the diffusion of O(3 P) atoms in a quantum solid. The O(3 P) atom mobility is detected by measuring the kinetics of the O(3 P) + O2 → O3 reaction after photolysis via infrared spectroscopy of the O3 reaction product. This reaction is barrierless and is thus assumed to be diffusion-controlled under these conditions such that the reaction rate constant can be used to estimate the oxygen atom diffusion coefficient. The O3 growth curves are well fit by single exponential expressions allowing the pseudo-first-order rate constant for the O(3 P) + O2 → O3 reaction to be extracted. The reaction rates are affected strongly by the p-H2 crystal morphology and display a non-Arrhenius-type temperature dependence consistent with quantum diffusion of the O(3 P) atom. The experimental results are compared to H(2 S) atom reaction studies in p-H2, analogous studies in noble gas matrices, and laboratory studies of atomic diffusion in astronomical ices and surfaces.