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.

12 pages including two embedded figures, accepted for publication in ApJ Letters