  We present a radio and X-ray study of PKS 1353-341, the brightest cluster
galaxy radio source at the center of a recent Chandra-discovered X-ray cluster.
Our multi-frequency VLA images reveal an edge-brightened (FR-II), double-lobed
structure with total ~50 kpc extent and 1.5 GHz power of $1.2\times10^{25}$ W
Hz$^{-1}$, separated from the bright, arcsecond-scale core. We reanalyzed the
Chandra data and found the X-ray emitting AGN is offset by ~9 kpc from a
compact X-ray cool-core with temperature, $kT=3.1\pm0.5$ keV, and a radius of
~22 kpc, surrounded by a hotter $kT=6.3\pm0.7$ keV gas out to ~50 kpc. The
offset suggests sloshing inside the cool-core induced by a minor merger or a
past outburst of the AGN that produced the large-scale radio lobes. The
comparable spatial scales of the lobes with the interface between the different
temperature X-ray plasma indicate the lobes are actively heating the outer
layers of what is now a remnant compact cool-core. Our dual-frequency VLBA
images reveal substructure in the central radio source, consisting of a radio
core with double-sided pc-scale jets pointing toward the kpc-scale structures.
The northern jet is detected only at 8.4 GHz, indicating its emission is behind
an absorbing torus or disk. We also measured faster apparent motions in the
southern jet up to $1.9\pm1.1c$ than in the northern jet ($0.8\pm0.5c$). While
the VLBA observations indicate the southern jet is aligned slightly closer to
our line of sight, the asymmetries are overall modest and imply minimal
projection effects in the large-scale radio structures.
