Large brains (relative to body size) might confer fitness benefits to animals. Although the putative costs of well-developed brains can constrain the majority of species to modest brain sizes, these costs are still poorly understood. Given that the neural tissue is energetically expensive and demands antioxidants, one potential cost of developing and maintaining large brains is increased oxidative stress (‘oxidation exposure’ hypothesis). Alternatively, because large-brained species exhibit slow-paced life histories, they are expected to invest more into self-maintenance such as an efficacious antioxidative defence machinery (‘oxidation avoidance’ hypothesis). We predict decreased antioxidant levels and/or increased oxidative damage in large-brained species in case of oxidation exposure, and the contrary in case of oxidation avoidance. We address these contrasting hypotheses for the first time by means of a phylogenetic comparative approach based on an unprecedented dataset of 4 redox state markers from 85 European bird species. Large-brained birds suffered less oxidative damage to lipids (measured as malondialdehyde levels) and exhibited higher total non-enzymatic antioxidant capacity than small-brained birds, while uric acid and glutathione levels were independent of brain size. These results were not altered by potentially confounding variables and did not depend on how relative brain size was quantified. Our findings partially support the ‘oxidation avoidance’ hypothesis and provide a physiological explanation for the linkage of large brains with slow-paced life histories: reduced oxidative stress of large-brained birds can secure brain functionality and healthy lifespan, which are integral to their lifetime fitness and slow-paced life history.