One hypothesis for the small size of insects relative to vertebrates, and the existence of giant fossil insects, is that atmospheric oxygen levels have constrained body sizes because oxygen delivery would be unable to match the needs of metabolically active tissues in larger insects. This study tested whether oxygen delivery becomes more challenging for larger insects by measuring the oxygen-sensitivity of flight metabolic rates and behavior during hovering for 11 different species of dragonflies that range in mass by an order of magnitude. Animals were flown in 7 different oxygen concentrations ranging from 30% to 2.5% to assess the sensitivity of their behavior and flight metabolic rates to oxygen. I also assessed the oxygen-sensitivity of flight in low-density air (nitrogen replaced with helium), to increase the metabolic demands of hovering flight. Lowered atmosphere densities did induce higher metabolic rates. Flight behaviors but not flight metabolic rates were highly oxygen-sensitive. A significant interaction between oxygen and mass was found for total flight time, with larger dragonflies varying flight time more in response to atmospheric oxygen. This study provides some support for the hypothesis that larger insects are more challenged in oxygen delivery, as predicted by the oxygen limitation hypothesis for insect gigantism in the Paleozoic.