We present a Chandra observation of the globular cluster Terzan 5 during times when the neutron-star X-ray transient EXO 1745–248 located in this cluster was in its quiescent state . We detected the quiescent system with a ( 0.5–10 keV ) luminosity of \sim 2 \times 10 ^ { 33 } ergs s ^ { -1 } . This is similar to several other neutron-star transients observed in their quiescent states . However , the quiescent X-ray spectrum of EXO 1745–248 was dominated by a hard power-law component instead of the soft component that usually dominates the quiescent emission of other neutron-star X-ray transients . This soft component could not conclusively be detected in EXO 1745–248 and we conclude that it contributed at most 10 % of the quiescent flux in the energy range 0.5–10 keV . EXO 1745–248 is only the second known neutron-star transient whose quiescent spectrum is dominated by the hard component ( SAX J1808.4–3658 is the other one ) . We discuss possible explanations for this unusual behavior of EXO 1745–248 , its relationship to other quiescent neutron-star systems , and the impact of our results on understanding quiescent X-ray binaries . We also discuss the implications of our results on the way the low-luminosity X-ray sources in globular clusters are classified .