  We present an archival analysis of Chandra X-ray observations for twelve
nearby early-type galaxies hosting radio sources with radio power $>10^{23} \,
\rm{W}~\rm{Hz}^{-1}$ at 1.4 GHz, similar to the radio power of the radio source
in NGC 4261. Previously, in a similar analysis of eight nearby X-ray and
optically-bright elliptical galaxies, Werner et al. 2012, found that NGC 4261
exhibited unusually low central gas entropy compared to the full sample. In the
central 0.3 kpc of NGC 4261, the ratio of cooling time to freefall time
($t_{\rm{cool}}/t_{\rm ff}$) is less than $10$, indicating that cold clouds may
be precipitating out of the hot ambient medium and providing fuel for accretion
in the central region. NGC 4261 also hosts the most powerful radio source in
the original sample. Because NGC 4261 may represent an important phase during
which powerful feedback from a central active galactic nucleus (AGN) is fueled
by multiphase condensation in the central kpc, we searched the Chandra archive
for analogs to NGC 4261. We present entropy profiles of those galaxies as well
as profiles of $t_{\rm{cool}}/t_{\rm ff}$. We find that one of them, IC 4296,
exhibits properties similar to NGC 4261, including the presence of only single
phase gas outside of $r \sim 2$ kpc and a similar central velocity dispersion.
We compare the properties of NGC 4261 and IC 4296 to hydrodynamic simulations
of AGN feedback fueled by precipitation. Over the course of those simulations,
the single phase galaxy has an entropy gradient that remains similar to the
entropy profiles inferred from our observations.
