We have studied the nuclear activity in a sample of six quiescent early-type galaxies , with new Chandra data and archival HST optical images . Their nuclear sources have X-ray luminosities \sim 10 ^ { 38 } – 10 ^ { 39 } erg s ^ { -1 } ( L _ { X } / L _ { Edd } \sim 10 ^ { -8 } – 10 ^ { -7 } ) , and colors or spectra consistent with accreting supermassive black holes ( SMBHs ) —except for the nucleus of NGC 4486B , which is softer than typical AGN spectra . In a few cases , the X-ray morphology of the nuclear sources shows hints of marginally extended structures , in addition to the surrounding diffuse thermal emission from hot gas , which is detectable on scales \gtrsim 1 kpc . In one case ( NGC 5845 ) , a dusty disk may partially obstruct our direct view of the SMBH . We have estimated the temperature and density of the hot interstellar medium , which is one major source of fuel for the accreting SMBH ; typical central densities are n _ { e } \approx ( 0.02 \pm 0.01 ) cm ^ { -3 } . Assuming that the hot gas is captured by the SMBH at the Bondi rate , we show that the observed X-ray luminosities are too faint to be consistent with standard disk accretion , but brighter than predicted by radiatively-inefficient solutions ( e.g. , advection-dominated acretion flows , ADAF ) . In total , there are \approx 20 galaxies for which SMBH mass , hot gas density , and nuclear X-ray luminosity are simultaneously known . In some cases , the nuclear sources are brighter than predicted by the ADAF model ; in other cases , they are consistent or fainter . We discuss the apparent lack of correlations between Bondi rate and X-ray luminosity , and suggest that , in order to understand the observed distribution , we need to know two additional parameters : the amount of gas supplied by the stellar population inside the accretion radius , and the fraction ( possibly \ll 1 ) of the total gas available that is accreted by the SMBH . We leave a detailed study of these issues to a subsequent paper .