  A deep Chandra observation of NGC 1265 (3C 83.1B), the prototype for the
narrow-angled-tailed (NAT) radio galaxy, reveals a small cool X-ray thermal
corona (~ 0.6 keV) embedded in the hot ICM of the Perseus cluster (~ 6.7 keV).
The corona is asymmetric with a sharp edge (~ 2.2'', or 0.8 kpc from the
nucleus) to the south and an extension to the north (at least ~ 8'' from the
nucleus), which is interpreted as the action of ram pressure while solely the
static ICM confinement is unable to explain. We estimate that the corona is
moving with a velocity of ~ 2.4 - 4.2 times the local sound speed to the south.
The presence of the sharp edge for this small corona indicates that the
transport processes are largely suppressed by the magnetic field there. The
magnetic field around the corona also suppresses heat conduction by at least a
factor of ~ 60 across the corona boundary. We conclude that it is unrealistic
to study the interaction of the small X-ray coronae with the hot ICM without
the consideration of the roles that magnetic field plays, a factor not included
in current simulations. An absorbed (N_H=1.5-3x10^22 cm^-2) nucleus is also
detected, which is not usual for FR I radio galaxies. Weak X-ray emission from
three inner radio knots in the jets is also detected. Indentations at the east
and west of the corona indicate interaction between the jets and the X-ray
corona. Narrow jets carry great amounts of energy out of the central AGN and
release the energy outside the corona, preserving the tiny and vulnerable
corona. This case reveals that the inner kpc core of the corona of massive
galaxies can survive both high-speed stripping and powerful AGN feedback. Thus,
the cooling of the X-ray coronae potentially provides fuel to the central SMBH
in rich environments where the amount of the galactic cold gas is at a minimum.
