A lightweight, modular chimney heat economizer adapted to replace a portion of the chimney for a combustion heat source in a building. The economizer includes a plurality of flue tubes having their ends welded to a pair of spaced apart tube sheets. Connected between the tube sheets and surrounding the flue tubes are inner and outer casings between which are sandwiched a layer of nonflammable insulation. The upper and lower tube sheets include outwardly extending flanges adapted to enable the economizer to be removeably secured in place so it may be easily installed and easily removed for maintenance and repair. The casings are provided with expansion joints. The top ends of the flue tubes may be flush with or recessed from the top surface of the upper tube sheet, and an upwardly projecting flange may surround the upper ends of the flue tubes to encourage condensed products from the combustion gases to drain into the flue pipes where they may be disposed of. The economizer may include baffles within the inner casing and may be adapted to have air circulated from top to bottom within the economizer to increase the thermal transfer from the flue pipes to the air circulated within the inner casing. A thermostat may be provided to maintain the temperature of the combustion gases in the flue tubes at about 350.degree. F. to prevent products in the combustion gases, and particularly creosote, from condensing in the flue tubes. The economizer may include a water heater.