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 \pm 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 \sim 60 ^ { \prime \prime } ( 240 kpc ) . We obtain the best fit beta model parameters of the surface brightness profile of \beta = 0.58 \pm 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 ) } = 3 \times 10 ^ { 44 } erg { s ^ { -1 } } and mass 1.5 \times 10 ^ { 14 } M _ { \odot } .