  In this Paper we report on our analysis of a ~25 ksec. Chandra X-ray
observation of the neutron star soft X-ray transient (SXT) 1H1905+000 in
quiescence. Furthermore, we discuss our findings of the analysis of optical
photometric observations which we obtained using the Magellan telescope and
photometric and spectroscopic observations which we obtained using the Very
Large Telescope at Paranal. The X-ray counterpart of 1H1905+000 was not
detected in our Chandra data, with a 95 per cent confidence limit to the source
count rate of 1.2x10^-4 counts s^-1. For different spectral models this yields
an upper limit on the luminosity of 1.8x10^31 erg s^-1 (for an upper limit on
the distance of 10 kpc.) This luminosity limit makes 1H1905+000 the faintest
neutron star SXT in quiescence observed to date. The neutron star luminosity is
so low that it is similar to the lowest luminosities derived for black hole
SXTs in quiescence. This low luminosity for a neutron star SXT challanges the
hypothesis presented in the literature that black hole SXTs in quiescence have
lower luminosities than neutron star SXTs as a result of the presence of a
black hole event horizon. Furthermore, the limit on the neutron star luminosity
obtained less than 20 years after the outburst has ceased, constrains the
thermal conductivity of the neutron star crust. Finally, the neutron star core
must be so cold that unless the time averaged mass accretion rate is lower than
2x10^-12 M_sun yr^-1, core cooling has to proceed via enhanced neutrino
emission processes. We derive a limit on the absolute I-band magnitude of the
quiescent counterpart of M_I>7.8 assuming the source is at 10 kpc. This is in
line with 1H1905+000 being an ultra-compact X-ray binary, as has been proposed
based on the low outburst V-band absolute magnitude.
