  The quasi-persistent neutron star X-ray transient and eclipsing binary EXO
0748-676 recently started the transition to quiescence following an accretion
outburst that lasted more than 24 years. We report on two Chandra and twelve
Swift observations performed within five months after the end of the outburst.
The Chandra spectrum is composed of a soft, thermal component that fits to a
neutron star atmosphere model with kT^inf~0.12 keV, joined by a hard powerlaw
tail that contributes ~20% of the total 0.5-10 keV unabsorbed flux. The
combined Chandra/Swift data set reveals a relatively hot and luminous quiescent
system with a temperature of kT^inf~0.11-0.13 keV and a bolometric thermal
luminosity of ~8.1E33-1.6E34 (d/7.4 kpc)^2 erg/s. We discuss our results in the
context of cooling neutron star models.
