We report high resolution imaging of the nucleus of the Seyfert 1 galaxy NGC 4151 obtained with a 50 ks Chandra HRC observation. The HRC image resolves the emission on spatial scales of 0.5", ~30 pc, showing an extended X-ray morphology overall consistent with the narrow line region (NLR) seen in optical line emission. Removal of the bright point-like nuclear source and image deconvolution techniques both reveal X-ray enhancements that closely match the substructures seen in the Hubble Space Telescope [OIII] image and prominent knots in the radio jet. We find that most of the NLR clouds in NGC 4151 have [OIII] to soft X-ray ratio ~10, despite the distance of the clouds from the nucleus. This ratio is consistent with the values observed in NLRs of some Seyfert 2 galaxies, which indicates a uniform ionization parameter even at large radii and a density decreasing as $r^{-2}$ as expected for a nuclear wind scenario. The [OIII]/X-ray ratios at the location of radio knots show an excess of X-ray emission, suggesting shock heating in addition to photoionization. We examine various mechanisms for the X-ray emission and find that, in contrast to jet-related X-ray emission in more powerful AGN, the observed jet parameters in NGC 4151 are inconsistent with synchrotron emission, synchrotron self-Compton, inverse Compton of CMB photons or galaxy optical light. Instead, our results favor thermal emission from the interaction between radio outflow and NLR gas clouds as the origin for the X-ray emission associated with the jet. This supports previous claims that frequent jet-ISM interaction may explain why jets in Seyfert galaxies appear small, slow, and thermally dominated, distinct from those kpc scale jets in the radio galaxies.