An absorption chiller system includes a generator section, a condenser section, an evaporator section and an absorber section all in fluid communication with each other and which operate to circulate a refrigerant therethrough. The evaporator section includes a transport membrane heat exchanger. The transport membrane heat exchanger includes a first and a second flow path. The first flow path is operable to flow the refrigerant therethrough under a vacuum pressure that is low enough to vaporize the refrigerant within the first flow path. The second flow path is operable to pass a fluid having water therethrough. Both water and heat are transferred from the fluid in the second flow path to the refrigerant in the first flow path through a membrane-based material of the transport membrane heat exchanger, such that the fluid passing through the second flow path has at least a portion of its water removed and is cooled.