We report results from our deep Chandra X-ray observations of a nearby radio galaxy, 4C+29.30 (z=0.0647). The Chandra image resolves structures on sub-arcsec to arcsec scales, revealing complex X-ray morphology and detecting the main radio features: the nucleus, a jet, hotspots, and lobes. The nucleus is absorbed (N(H)=3.95 (+0.27/-0.33)x10^23 atoms/cm^2) with an unabsorbed luminosity of L(2-10 keV) ~ (5.08 +/-0.52) 10^43 erg/s characteristic of Type 2 AGN. Regions of soft (<2 keV) X-ray emission that trace the hot interstellar medium (ISM) are correlated with radio structures along the main radio axis indicating a strong relation between the two. The X-ray emission beyond the radio source correlates with the morphology of optical line-emitting regions. We measured the ISM temperature in several regions across the galaxy to be kT ~ 0.5 with slightly higher temperatures (of a few keV) in the center and in the vicinity of the radio hotspots. Assuming these regions were heated by weak shocks driven by the expanding radio source, we estimated the corresponding Mach number of 1.6 in the southern regions. The thermal pressure of the X-ray emitting gas in the outermost regions suggest the hot ISM is slightly under-pressured with respect to the cold optical-line emitting gas and radio-emitting plasma, which both seem to be in a rough pressure equilibrium. We conclude that 4C+29.30 displays a complex view of interactions between the jet-driven radio outflow and host galaxy environment, signaling feedback processes closely associated with the central active nucleus.