We present the analysis of the 93 ksec Chandra ACIS–S data for the galaxy CGCG 292–057 (z = 0.054), with complex radio structure indicative of the intermittent jet activity. In order to characterize precisely the spectrum of the unresolved low-luminosity active nucleus in the source, we performed detailed MARX/PSF simulations and studied the radial profile of the source region surface brightness. In this way, we have detected an additional X-ray component extending from a few up to ∼10 kpc from the unresolved core, which could be associated with the hot gaseous medium compressed and heated (up to 0.9 keV) by the expanding inner lobes of the radio galaxy. We modeled the X-ray spectrum of the unresolved nucleus assuming various emission models, including an absorbed power-law, a power-law plus thermal emission component, and a two-temperature thermal plasma. The best fit was however obtained assuming a power-law emission scattered by a hot ionized gas, giving rise to the 6.7 keV iron line.