We have investigated analytically the performance of the thermally driven, advanced three-stage adsorption chiller utilizing low-grade waste heat of 50 degrees C and lower temperatures as the driving heat source, in combination with a heat sink (cooling water) of 30 degrees C. The closed cycle chiller for use in air-conditioning utilizes the silica-gel-water adsorption system. A cycle-simulation program was constructed to analyze the influence of operating conditions (temperatures, flow rates and adsorption-desorption cycle times) on cooling output, COP and chiller efficiency (eta = COP/Carnot COP). The main advantage of this chiller is that it is operational with smaller regenerating temperature lifts (Delta T-regen = heat source-heat sink temperature) than other heat-driven chillers. By cycle simulation, it was shown that the three-stage chiller can be operated with heat sources of 50 and 40 degrees C in combination with cooling sources of 39 and 30 degrees C, respectively. The simulation results also show that for the chiller to operate effectively, heat sources of 50 degrees C require cooling sources between 35 and 20 degrees C (Delta T-regen = 15 to about 30K), while heat sources of 40 degrees C need cooling sources in the range of 28-20 degrees C (Delta T-regen = 12 to about 20K).