We report on spectroscopic imaging observations of the nearby (z=0.022) galaxy cluster 3C 129 performed with the ACIS detector on board of the Chandra X-ray observatory. Applying a deprojection analysis which fully takes into account the spatially resolved X-ray energy spectra we investigate the radial variation of temperature and particle density of the Intracluster Medium (ICM). While earlier data indicated a weak cooling flow and a cool cluster core, the Chandra data suggests that the core is hotter than the rest of the cluster: at the center we infer (7.9+4.4-2.4) keV while the mean temperature of all the other ICM shells is (5.1+-0.3) keV (all errors on 90% confidence level). Based on the radial entropy profile we discuss the evidence for shock heating of the ICM at the cluster center. We discuss the possibility to use imaging spectroscopy data of more regular clusters to extract maps of the gravitational dark matter potential.