  Elliptical galaxy nuclei are the sites of the largest black holes known, but
typically show little or no nuclear activity. We investigate this extreme
quiescence using Chandra X-ray Observatory observations of the giant elliptical
galaxies NGC 1399, NGC 4472, and NGC 4636. The unique Chandra imaging power
enables us to place upper limits of 7.3, 15 and 28 X 10^-9 the Eddington
luminosity for the 0.1-1 billion solar mass black holes in NGC 1399, NGC 4472,
and NGC 4636, respectively. The corresponding radiative efficiencies in this
band are 4.1, 24, and 620 X 10^-6 using Bondi accretion rates derived from the
Chandra hot interstellar gas surface brightness profiles. These limits are
inconsistent with basic advection-dominated accretion flow (ADAF) models for
NGC 1399 and NGC 4472, indicating accretion onto the black hole at 10% of the
Bondi rate.
