For cosmic particle spectroscopy on the International Space Station the AMS experiment will be equipped with a Transition Radiation Detector to improve proton background supression up to 300 GeV. The TRD has 20 layers of fleece radiator with Xe/CO2 proportional-mode straw-tube chambers. They are supported in a conically shaped octagon structure made of CFC-Al-honeycomb. For low power consumption VA analog multiplexers are used as front-end readout. A 20 layer prototype has achieved proton rejections above 100 at 90% electron efficiency for beam energies up to 250 GeV. The detector is under construction at RWTH Aachen, the gas system will be built at MIT, slow-control and DAQ at TH Karlsruhe.