  EXO 1745-248 is a transient neutron-star low-mass X-ray binary that resides
in the globular cluster Terzan 5. We studied the transient during its quiescent
state using 18 Chandra observations of the cluster acquired between 2003 and
2016. We found an extremely variable source, with a luminosity variation in the
0.5-10 keV energy range of $\sim3$ orders of magnitude (between
$3\times10^{31}$ erg s$^{-1}$ and $2\times10^{34}$ erg s$^{-1}$) on timescales
from years down to only a few days. Using an absorbed power-law model to fit
its quiescent spectra, we obtained a typical photon index of $\sim1.4$,
indicating that the source is even harder than during outburst and much harder
than typical quiescent neutron stars if their quiescent X-ray spectra are also
described by a single power-law model. This indicates that EXO 1745-248 is very
hard throughout the entire observed X-ray luminosity range. At the highest
luminosity, the spectrum fits better when an additional (soft) component is
added to the model. All these quiescent properties are likely related to strong
variability in the low-level accretion rate in the system. However, its extreme
variable behavior is strikingly different from the one observed for other
neutron star transients that are thought to still accrete in quiescence. We
compare our results to these systems. We also discuss similarities and
differences between our target and the transitional millisecond pulsar IGR
J18245-2452, which also has hard spectra and strong variability during
quiescence.
