  Using the Chandra X-ray Observatory, we have detected the black hole
transients V4641 Sgr and XTE J1859+226 in their low luminosity, quiescent
states. The 0.3-8 keV luminosities are (4.0^(+3.3)_(-2.4))E31 (d/7 kpc)^2 erg/s
and (4.2^(+4.8)_(-2.2))E31 (d/11 kpc)^2 erg/s for V4641 Sgr and XTE J1859+226,
respectively. With the addition of these 2 systems, 14 out of the 15 transients
with confirmed black holes (via compact object mass measurements) now have
measured quiescent luminosities or sensitive upper limits. The only exception
is GRS 1915+105, which has not been in quiescence since its discovery in 1992.
The luminosities for V4641 Sgr and XTE J1859+226 are consistent with the median
luminosity of 2E31 erg/s for the systems with previous detections. Our analysis
suggests that the quiescent X-ray spectrum of V4641 Sgr is harder than for the
other systems in this group, but, due to the low statistical quality of the
spectrum, it is not clear if V4641 Sgr is intrinsically hard or if the column
density is higher than the interstellar value. Focusing on V4641 Sgr, we
compare our results to theoretical models for X-ray emission from black holes
in quiescence. Also, we obtain precise X-ray positions for V4641 Sgr and XTE
J1859+226 via cross-correlation of the X-ray sources detected near our targets
with IR sources in the 2 Micron All-Sky Survey catalog.
