  We report the results of observations of the black hole binaries XTE
J1550-564 and H 1743-322 in their quiescent state using the Chandra X-ray
Observatory. Both sources are detected at their faintest level of X-ray
emission ever observed with a 0.5-10 keV unabsorbed luminosity of 2 $\times$
10$^{32}$ (d/5 kpc)$^2$ erg s$^{-1}$ for XTE J1550-564 and 9 $\times$ 10$^{31}$
(d/8 kpc)$^2$ erg s$^{-1}$ for H 1743-322. These luminosities are in the upper
range compared to the faintest levels observed in other black hole systems,
possibly related to residual accretion for these sources with frequent
outbursts. For XTE J1550-564, the Chandra observations also constrain the X-ray
spectrum as a fit with an absorbed power-law model yields a photon index of
2.25 $\pm$ 0.08, clearly indicating a softening of the X-ray spectrum at lower
luminosities compared to the standard hard state. Similar softening at low
luminosity is seen for several black hole transients with orbital periods less
than 60 hours. Most of the current models of accreting black holes are able to
reproduce such softening in quiescence. In contrast, we find that systems with
orbital periods longer than 60 hours appear to have hard spectra in quiescence
and their behaviour may be consistent with hardening in quiescence.
