  We present the analysis of a 35 ksec long Chandra observation of the neutron
star soft X-ray transient (SXT) SAX J1810.8-2609. We detect three sources in
the field of view. The position of one of them is consistent with the location
of the ROSAT error circle of SAX J1810.8-2609. The accurate Chandra position of
that source coincides with the position of the proposed optical counterpart,
strengthening the identification as the counterpart. We detected the neutron
star SXT system in quiescence at an unabsorbed luminosity of ~1x10^32 erg s^-1
(assuming a distance of 4.9 kpc). This luminosity is at the low-end of
quiescent luminosities found in other neutron star SXTs. This renders support
to the existence of a group of faint soft X-ray transients of which the
accreting millisecond X-ray pulsar SAX J1808.4-3658 is the most prominent
member. The quiescent spectrum of SAX J1810.8-2609 is well-fit with an absorbed
power law with photon index of 3.3+-0.5. With a value of 3.3x10^21 cm^-2 the
Galactic absorption is consistent with the value derived in outburst. Since the
spectra of quiescent neutron star SXTs are often fit with an absorbed blackbody
or neutron star atmosphere plus power-law model we also fitted the spectrum
using those fit functions. Both models provide a good fit to the data. If
cooling of the neutron star core and/or crust is responsible for the soft part
of the spectrum the time averaged mass accretion rate must have been very low
(~5.7x10^-13 Msun yr^-1; assuming standard core cooling only) or the neutron
star must be massive. We also discuss the possibility that the thermal spectral
component in neutron stars in quiescence is produced by residual accretion.
