The AMS 02 experiment will be installed on the International Space Station ISS to measure the cosmic ray spectrum with unprecedented accuracy. Dark matter and SUSY searches will rely on positron spectroscopy free from proton background for particle energies up to 300 GeV. In combination with an ECAL the Transition Radiation Detector is required to reject protons to better than 10**-2 at 90% positron efficiency. Building a TRD to meet these requirements for a spectrometer scheduled to operate for three years in space is a challenge for design and construction.