Conventional solar heat-driven single stage two bed chillers demand a large area for installation of solar thermal collector to activate the chiller, but in a highly populated tropical country open spaces is insufficient. In the intention to utilize accessible solar energy with better performance, a mathematical investigation is carried out with a three bed adsorption cooling unit working with silica gel-water pair. The studied chiller is powered by direct solar heat collected by a series of compound parabolic concentrator solar thermal collectors without any heat or mass recovery. The working principal of the chiller is, in principle, the same as the conventional two-bed adsorption chiller. However, instead of two half cycles, there are three one third cycles in the proposed chiller in which at every cycle the former desorber is kept in the precooling mode and as an adsorber for the next two one third cycles, respectively. As desorption kinetic is faster than the adsorption kinetics, this longer precooling mode helps the silica gel granules to adsorb more water molecules and increase evaporation rate. Hence, a better cooling effect of at least 1 degrees C can be observed, increases chiller working hour after sunset for almost a further one hour.