Storage of photovoltaic and wind electricity in batteries could solve the mismatch problem between the intermittent supply of these renewable resources and variable demand. Flow batteries permit more economical long-duration discharge than solid-electrode batteries by using liquid electrolytes stored outside of the battery. We report an alkaline flow battery based on redox-active organic molecules that are composed entirely of Earth-abundant elements and are nontoxic, nonflammable, and safe for use in residential and commercial environments. The battery operates efficiently with high power density near room temperature. These results demonstrate the stability and performance of redox-active organic molecules in alkaline flow batteries, potentially enabling cost-effective stationary storage of renewable energy.