The lithium-ion batteries that ushered in the wireless revolution rely on electrode strategies that are being stretched to power electric vehicles. Low-cost, safe electrical-energy storage that enables better use of alternative energy sources (e.g., wind, solar, and nuclear) requires an alternative strategy. We report a demonstration of the feasibility of a battery having a thin, solid alkali-ion electrolyte separating a water-soluble redox couple as the cathode and lithium or sodium in a nonaqueous electrolyte as the anode. The cell operates without a catalyst and has high storage efficiency. The possibility of a flow-through mode for the cathode allows flexibility of the cell design for safe, large-capacity electrical-energy storage at an acceptable cost.