  We have observed the quasi-persistent neutron-star X-ray transient and
eclipsing binary MXB 1659-29 in quiescence on three occasions with Chandra. The
purpose of our observations was to monitor the quiescent behavior of the source
after its last prolonged (~2.5 years) outburst which ended in September 2001.
The X-ray spectra of the source are consistent with thermal radiation from the
neutron-star surface. We found that the bolometric flux of the source decreased
by a factor of 7-9 over the time-span of 1.5 years between our first and last
Chandra observations. The effective temperature also decreased, by a factor of
1.6-1.7. The decrease in time of the bolometric flux and effective temperature
can be described using exponential decay functions, with e-folding times of 0.7
and ~3 years, respectively. Our results are consistent with the hypothesis that
we observed a cooling neutron-star crust which was heated considerably during
the prolonged accretion event and which is still out of thermal equilibrium
with the neutron-star core. We could only determine upper-limits for any
luminosity contribution due to the thermal state of the neutron-star core. The
rapid cooling of the neutron-star crust implies that it has a large thermal
conductivity. Our results also suggest that enhanced cooling processes are
present in the neutron-star core.
