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 \times 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 .
We predict that large area surveys of the Milky Way should also turn up large numbers of quiescent X-ray binaries .