We report on the first X-ray observations of the neutron star soft X-ray transient ( SXT ) XTE J2123–058 in quiescence , made by the Chandra X-ray Observatory and BeppoSAX , as well as contemporaneous optical observations . In 2002 , the Chandra spectrum of XTE J2123–058 is consistent with a power-law model , or the combination of a blackbody plus a power-law , but it is not well-described by a pure blackbody . Using the interstellar value of N _ { H } , the power-law fit gives \Gamma = 3.1 ^ { +0.7 } _ { -0.6 } and indicates a 0.3–8 keV unabsorbed luminosity of ( 9 ^ { +4 } _ { -3 } ) \times 10 ^ { 31 } ( d /8.5 kpc ) ^ { 2 } ergs s ^ { -1 } ( 90 % confidence errors ) . Fits with models consisting of thermal plus power-law components indicate that the upper limit on the temperature of a 1.4 M _ { \mathord { \odot } } , 10 km radius neutron star with a hydrogen atmosphere is kT _ { eff } < 66 eV , and the upper limit on the unabsorbed , bolometric luminosity is L _ { \infty } < 1.4 \times 10 ^ { 32 } ergs s ^ { -1 } , assuming d = 8.5 kpc . Of the neutron star SXTs that exhibit short ( < 1 year ) outbursts , including Aql X-1 , 4U 1608–522 , Cen X-4 , and SAX J1810.8–2609 , the lowest temperatures and luminosities are found for XTE J2123–058 and SAX J1810.8–2609 . From the BeppoSAX observation of XTE J2123–058 in 2000 , we obtained an upper limit on the 1–10 keV unabsorbed luminosity of 9 \times 10 ^ { 32 } ergs s ^ { -1 } . Although this upper limit allows that the X-ray luminosity may have decreased between 2000 and 2002 , that possibility is not supported by our contemporaneous R -band observations , which indicate that the optical flux increased significantly . Motivated by the theory of deep crustal heating by Brown and co-workers , we characterize the outburst histories of the five SXTs . The low quiescent luminosity for XTE J2123–058 is consistent with the theory of deep crustal heating without requiring enhanced neutron star cooling if the outburst recurrence time is \mathrel { \lower 3.44 pt \hbox { \hbox to 0.0 pt { $ \sim$ } \raise 3.87 pt \hbox { $ > $ } } } 70 years .