The rising population has boosted energy demand, with the cooling sector emerging as a major contributor, leading to increased emissions due to the use of fossil fuel-based electricity. Solar-driven cooling presents a sustainable alternative, yet it is limited by the intermittent nature of solar radiation. Cold Thermal Energy Storage (CTES) can address this challenge by enabling continuous cooling beyond sun hours. Each conventional CTES method, including sensible, latent, and thermochemical, has limitations regarding energy density, cost, and system complexity. This study proposes a solar-driven two-bed chemical adsorption refrigeration system integrated with a natural refrigerant-based CTES. Using calcium chloride–ammonia as the working pair, where ammonia serves as both refrigerant and storage medium. The ammonia is actively stored as a liquid at ambient temperature in a storage tank. This separate refrigerant delivery from bed operation ensures continuous on-demand subzero cooling. A MATLAB-based quasi-steady-state simulation, incorporating real ambient conditions from a refrigerated warehouse in Beijing, demonstrated the system’s capability to consistently deliver 432 kWh of cooling per day. During daytime operation, the system delivers a cooling load of 234 kWh while simultaneously storing 198 kWh of cold thermal energy for utilization during nighttime hours. The system achieved a COP of 0.402 without requiring compressors or high-grade heat. A parametric analysis was conducted to assess system performance under varying evaporator, condenser, desorption, and ambient temperatures.