  Chandra observations of low-luminosity supermassive black holes in nearby
elliptical galaxies provide tight limits on both their nuclear luminosities and
on their Bondi accretion rates. We examine Chandra constraints on NGC 6166, the
dominant galaxy in the cluster Abell 2199, which hosts a \sim 10^9 \Msun black
hole. We measure a nuclear X-ray luminosity L_{x} \sim 10^{40} erg/s and show
that the density and temperature profiles of the hot interstellar medium imply
a Bondi accretion rate of Mdot_{Bondi} \sim 3 10^{-2} Msun/yr. This accretion
rate predicts a nuclear luminosity of \sim 10^{44} erg/s for a canonical
radiative efficiency of 10%. Unless the Bondi estimate is inappropriate and/or
the accretion rate onto the black hole is significantly reduced, the observed
nuclear flux constrains the radiative efficiency of the accretion flow to be
\eta \sim 10^{-5}. We show that low-radiative efficiency accretion flows with
radial density profiles \rho \approxpropto r^{-3/2} (and not significantly
flatter) can explain the observed nuclear X-ray luminosity but that the power
output from the jets in NGC 6166 is also important to the energetics of the
system.
