  We present results from a deep (174 ks) Chandra observation of the FR-II
radio galaxy 3C 220.1, the central brightest cluster galaxy (BCG) of a $kT
\sim$ 4 keV cluster at $z=0.61$. The temperature of the hot cluster medium
drops from $\sim5.9$ keV to $\sim3.9$ keV at $\sim$ 35 kpc radius, while the
temperature at smaller radii may be substantially lower. The central active
galactic nucleus (AGN) outshines the whole cluster in X-rays, with a bolometric
luminosity of $2.0\times10^{46}$ erg s$^{-1}$ ($\sim10$% of the Eddington
rate). The system shows a pair of potential X-ray cavities $\sim35$ kpc east
and west of the nucleus. The cavity power is estimated within the range of
$1.0\times10^{44}$ erg s$^{-1}$ and $1.7\times10^{45}$ erg s$^{-1}$, from
different methods. The X-ray enhancements in the radio lobes could be due to
inverse Compton emission, with a total 2-10 keV luminosity of
$\sim8.0\times10^{42}$ erg s$^{-1}$. We compare 3C 220.1 with other cluster
BCGs, including Cygnus A, as there are few BCGs in rich clusters hosting an
FR-II galaxy. We also summarize the jet power of FR-II galaxies from different
methods. The comparison suggests that the cavity power of FR-II galaxies likely
under-estimates the jet power. The properties of 3C 220.1 suggest that it is at
the transition stage from quasar-mode feedback to radio-mode feedback.
