Hydroxyl, OH, is the main oxidant in the lower atmosphere and determines how long methane and most other trace gases remain in the atmosphere, thereby controlling the amount of greenhouse warming produced by these gases. It is not well known how this oxidizer has changed in the past, or how it will change in the future. Reconstructions of ¹⁴CO concentration ([¹⁴CO]) from ice cores at sites with very high snowfall rates can provide such constraints. Air was sampled from the high snowfall site Law Dome, Antarctica to a depth of 240 meters, allowing perspective on hydroxyl from about 1866 to present. Chemical climate modeling aids interpretation of ice core air samples, and together they show that long-term Southern Hemisphere hydroxyl variability over the industrial period is small, indicating that hydroxyl is likely stable even at times of large changes in abundances of reactive species in the atmosphere.