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A xenon multiwire position-sensitive proportional counter (PSPC) with a high degree of long-term stability has been constructed and tested in detail. It is suitable for a 0.1 to 10 keV X-ray telescope such as AXAF, which it would share with detectors having better spatial and spectral resolution. Compared to other detectors, the larger format, higher quantum efficiency, and lower background of the PSPC makes it generally the most useful instrument for observations of diffuse cosmic X-ray sources and associations of sources more extended than a few tenths of a degree in diameter. Given the good spatial linearity, the systematic uncertainty for source locations is finer than an arcsecond. The spatial resolution varies as 0.3 mm/exp 0.5 (keV) over the range 0.2-4 keV, in accordance with theoretical limits determined by the size and the number of electrons in the primary charge cloud.