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 } ) \times 10 ^ { 31 } ( d /7 kpc ) ^ { 2 } erg s ^ { -1 } and ( 4.2 ^ { +4.8 } _ { -2.2 } ) \times 10 ^ { 31 } ( d /11 kpc ) ^ { 2 } erg s ^ { -1 } 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 2 \times 10 ^ { 31 } erg s ^ { -1 } 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 .