We report the results of a deep Chandra survey of the Sculptor dwarf spheroidal galaxy. We find five X-ray sources with L_X of at least 6*10^33 ergs/sec with optical counterparts establishing them as members of Sculptor. These X-ray luminosities indicate that these sources are X-ray binaries, as no other known class of Galactic point sources can reach 0.5-8 keV luminosities this high. Finding these systems proves definitively that such objects can exist in an old stellar population without stellar collisions. Three of these objects have highly evolved optical counterparts (giants or horizontal branch stars), as do three other sources whose X-ray luminosities are in the range which includes both quiescent low mass X-ray binaries and the brightest magnetic cataclysmic variables. Large area surveys should also turn up large numbers of quiescent X-ray binaries. (Modified)
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