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Damage caused by implanted helium (He) is a major concern for material performance in future nuclear reactors. We use a combination of experiments and modeling to demonstrate that amorphous silicon oxycarbide (SiOC) is immune to He-induced damage. By contrast with other solids, where implanted He becomes immobilized in nanometer-scale precipitates, He in SiOC remains in solution and outgasses from the material via atomic-scale diffusion without damaging its free surfaces. Furthermore, the behavior of He in SiOC is not sensitive to the exact concentration of carbon and hydrogen in this material, indicating that the composition of SiOC may be tuned to optimize other properties without compromising resistance to implanted He.