Stem cells reside in specialized microenvironments known as niches. During Drosophila development, glial cells provide a niche that sustains the proliferation of neural stem cells (neuroblasts) during starvation. We now find that the glial cell niche also preserves neuroblast proliferation under conditions of hypoxia and oxidative stress. Lipid droplets that form in niche glia during oxidative stress limit the levels of reactive oxygen species (ROS) and inhibit the oxidation of polyunsaturated fatty acids (PUFAs). These droplets protect glia and also neuroblasts from peroxidation chain reactions that can damage many types of macromolecules. The underlying antioxidant mechanism involves diverting PUFAs, including diet-derived linoleic acid, away from membranes to the core of lipid droplets, where they are less vulnerable to peroxidation. This study reveals an antioxidant role for lipid droplets that could be relevant in many different biological contexts.