Earth's atmosphere oxidizes the greenhouse gas methane and other gases, thus determining their lifetimes and oxidation products. Much of this oxidation occurs in the remote, relatively clean free troposphere above the planetary boundary layer, where the oxidation chemistry is thought to be much simpler and better understood than it is in urban regions or forests. The NASA airborne Atmospheric Tomography study (ATom) was designed to produce cross sections of the detailed atmospheric composition in the remote atmosphere over the Pacific and Atlantic Oceans during four seasons. As part of the extensive ATom data set, measurements of the atmosphere's primary oxidant, hydroxyl (OH), and hydroperoxyl (HO2) are compared to a photochemical box model to test the oxidation chemistry. Generally, observed and modeled median OH and HO2 agree to within combined uncertainties at the 2σ confidence level, which is ~±40%. For some seasons, this agreement is within ~±20% below 6‐km altitude. While this test finds no significant differences, OH observations increasingly exceeded modeled values at altitudes above 8 km, becoming ~35% greater, which is near the combined uncertainties. Measurement uncertainty and possible unknown measurement errors complicate tests for unknown chemistry or incorrect reaction rate coefficients that would substantially affect the OH and HO2 abundances. Future analysis of detailed comparisons may yield additional discrepancies that are masked in the median values. Plain Language Summary Chemistry in the vast, remote atmosphere destroys methane and other greenhouse gases. This chemistry is thought to be simple and well understood compared to that in polluted cities or in forests. From the NASA airborne Atmospheric Tomography study over remote oceans, comparisons of observed and modeled reactive gases show that the chemistry is generally understood to within the uncertainties of the measurement and model. However, for the atmosphere's primary reactive gas, hydroxyl, measured values exceed modeled values in the upper troposphere, pointing to errors in probably the measurements but possibly the model chemistry.