A c harged-particle tracking chamber consisting of about 1400 individual drift tubes `straws' has been designed and built for the experiment PS202 JETSET , installed in the antiproton storage ring LEAR at CERN. The design considerations, the development o f s e v eral new techniques, and the construction of the detector are described. A complex system of front-end electronics, specially developed for the chamber, provides drift-time as well as charge-division measurements. Calibration procedures for obtaining three-dimensional space information for charged-particle tracks are described. The performance of the chamber achieved in the actual experiment is discussed.