[en] We present a 70 ks Chandra observation of the radio galaxy 3C 293. This galaxy belongs to the class of molecular hydrogen emission galaxies (MOHEGs) that have very luminous emission from warm molecular hydrogen. In radio galaxies, the molecular gas appears to be heated by jet-driven shocks, but exactly how this mechanism works is still poorly understood. With Chandra, we observe X-ray emission from the jets within the host galaxy and along the 100 kpc radio jets. We model the X-ray spectra of the nucleus, the inner jets, and the X-ray features along the extended radio jets. Both the nucleus and the inner jets show evidence of 10⁷ K shock-heated gas. The kinetic power of the jets is more than sufficient to heat the X-ray emitting gas within the host galaxy. The thermal X-ray and warm H₂ luminosities of 3C 293 are similar, indicating similar masses of X-ray hot gas and warm molecular gas. This is consistent with a picture where both derive from a multiphase, shocked interstellar medium (ISM). We find that radio-loud MOHEGs that are not brightest cluster galaxies (BCGs), like 3C 293, typically have $L_{{\mathrm{H}}_2}/L_X\sim <!--\; ???\; -->1$ and $M_{{\mathrm{H}}_2}/M_X\sim <!--\; ???\; -->1$, whereas MOHEGs that are BCGs have $L_{{\mathrm{H}}_2}/L_X\sim <!--\; ???\; -->0.01$ and $M_{{\mathrm{H}}_2}/M_X\sim <!--\; ???\; -->0.01$. The more massive, virialized, hot atmosphere in BCGs overwhelms any direct X-ray emission from current jet-ISM interaction. On the other hand, $L_{{\mathrm{H}}_2}/L_X\sim <!--\; ???\; -->1$ in the Spiderweb BCG at z = 2, which resides in an unvirialized protocluster and hosts a powerful radio source. Over time, jet-ISM interaction may contribute to the establishment of a hot atmosphere in BCGs and other massive elliptical galaxies.