Current cooling technologies primarily rely on electricity generated from fossil fuels, contributing to global warming. Consequently, there is an urgent need to transition towards sustainable cooling technologies. In response to this challenge, this study proposes and analyzes a combined cooling and cold thermal energy storage system utilizing a solid-gas thermochemical sorption process. The aim is to meet the cooling demand of a building using solar energy, eliminating the use of fossil fuel-based electricity. Solar energy available during the daytime is used to produce cooling and store surplus cold thermal energy. The stored cold thermal energy is utilized during nighttime when solar energy is not available. Cooling is produced by evaporation of liquid refrigerant while the cold energy storage is achieved by storing surplus liquid refrigerant (ammonia) for later use. A steady-state thermodynamic model is developed to study the performance of the proposed system. To demonstrate the operating strategy of the proposed system, the cooling demand of a building is considered as a case study. The average COP of the proposed system is estimated. An average COP of 0.42 is estimated for the proposed system at a heat source temperature of 100 °C and an evaporating temperature of 0 °C. The analysis of the present case can be effectively used to provide the cooling load of a building without dependency on electricity.