A new approach for solar electricity generation and storage is proposed, based on the concept of thermally regenerative batteries. Concentrated sunlight is used for external thermo-chemical charging of a flow battery, and electricity is produced by conventional electro-chemical discharge of the battery. The battery replaces the steam turbine, currently used in commercial concentrated solar power (CSP) plants, potentially leading to much higher conversion efficiency. This approach offers potential performance, cost and operational advantages compared to existing solar technologies, and to existing storage solutions for management of an electrical grid with a significant contribution of intermittent solar electricity generation. Here we analyze the theoretical conversion efficiency for new thermo-electro-chemical storage (TECS) plant schemes based on the electro-chemical systems of sodium-sulfur (Na-S) and zinc-air. The thermodynamic upper limit of solar to electricity conversion efficiency for an ideal TECS cycle is about 60% for Na-S at reactor temperature of 1550K, and 65% for the zinc-air system at 1750K, both under sunlight concentration of 3000. A hybrid process with carbothermic reduction in the zinc-air system reaches 60% theoretical efficiency at the more practical conditions of reaction temperature <1200K and concentration <1000. Practical TECS plant efficiency, estimated from these upper limits, may then be much higher compared to existing solar electricity technologies. The technical and economical feasibility of the proposed cycle are also discussed.