  We discovered an X-ray cluster in a Chandra observation of the compact steep
spectrum (CSS) radio source 1321+045 (z=0.263). CSS sources are thought to be
young radio objects at the beginning of their evolution and can potentially
test the cluster heating process. 1321+045 is a relatively low luminosity
source and its morphology consists of two radio lobes on the opposite sides of
a radio core with no evidence for jets or hotspots. The optical emission line
ratios are consistent with an interstellar medium (ISM) dominated by
AGN-photoionization with a small contribution from star formation, and no
contributions from shocks. Based on these ratios, we classify 1321+045 as a low
excitation galaxy (LEG) and suggest that its radio activity is in a coasting
phase. The X-ray emission associated with the radio source is detected with
36.1+/-8.3 counts, but the origin of this emission is highly uncertain. The
current X-ray image of the cluster does not show any signatures of a radio
source impact on the cluster medium. Chandra detects the cluster emission at >3
sigma level out to ~60 arcsec (~240 kpc). We obtain the best fit beta model
parameters of the surface brightness profile of beta=0.58+/-0.2 and a core
radius of 9.4^{+1.1}_{-0.9} arcsec. The average temperature of the cluster is
equal to kT=4.4^{+0.5}_{-0.3} keV, with a temperature and cooling profile
indicative of a cooling core. We measure the cluster luminosity L_(0.5-2
keV)=3x10^{44} erg s^{-1} and mass 1.5x10^{14} M_sun.
