We propose a physical mechanism for the transport of oxidants formed at the surface of icy moons or exoplanets by irradiation of ice into their internal oceans. This oxidant flux is important for the redox state of the internal ocean and hence its habitability. Our work is motivated by Jupiter’s moon Europa but may have applications to other icy moons and exoplanets. On Europa we propose that the drainage of near-surface brines formed during the formation of chaotic terrains can transport oxidant through the ice shell and deliver oxidants to the internal ocean. We estimate that Europa’s regolith contains approximately 1016 mols of O2 formed by irradiation. If these oxidants are mixed into the brines that are generated during the formation of chaotic terrains, then brine migration can deliver 85% of the surface oxidants to the ocean on time scales of 104 years, see Figure. In this process, the rate of oxidant delivery is therefore limited by the formation of chaotic terrains rather than the brine migration. Given that one quarter of Europa’s surface is classified as chaos and Europa’s mean surface age of 40-90 million years, we estimate that the rate of O2 delivery to the ocean is approximately 108 mol/yr. This is lower than previous estimates, which assume that the entire inventory of surface oxidants is delivered to the ocean due to complete overturn of the ice shell. The process we envision does not require overturn of the ice shell but requires the formation of near surface brines facilitated by the presence of impurities. If these conditions are met on other icy moons or exoplanets brine drainage may also provide an oxidant flux into internal oceans.