An air-conditioning system with thermal storage system for storing cooling capacity. The storage system comprises a quantity of fill material that preferably comprises water or similar liquid that is located in a cavity in the ground. The fill material may also include a bed of gravel with the pool of liquid filling the void spaces in the gravel. Sidewalls of the cavity are preferably supported primarily by the mechanical properties of the earth and the fill material. The lower boundary of the cavity is impermeable liner. A cover that blocks solar radiation and preferably with thermal insulation covers the top of the fill material. A chiller and a pump supply cooled liquid during night or other times of reduced electrical costs and liquid from the storage flows through a liquid-to-air heat exchanger during peak demand periods.