We present results of an ~20-ks X-ray observation of the Wolf-Rayet (WR) binary system WR 147 obtained with XMM-Newton. Previous studies have shown that this system consists of a nitrogen-type WN8 star plus an OB companion whose winds are interacting to produce a colliding wind shock. X-ray spectra from the pn and MOS detectors confirm the high extinction reported from infrared studies and reveal hot plasma including the first detection of the Fe Kα line complex at 6.67 keV. Spectral fits with a constant-temperature plane-parallel shock model give a shock temperature kTshock = 2.7 keV (Tshock ~ 31 MK), close to but slightly hotter than the maximum temperature predicted for a colliding wind shock. Optically thin plasma models suggest even higher temperatures, which are not yet ruled out. The X-ray spectra are harder than can be accounted for using 2D numerical colliding wind shock models based on nominal mass-loss parameters. Possible explanations include: (i) underestimates of the terminal wind speeds or wind abundances, (ii) overly simplistic colliding wind models or (iii) the presence of other X-ray emission mechanisms besides colliding wind shocks. Further improvement of the numerical models to include potentially important physics such as non-equilibrium ionization will be needed to rigorously test the colliding wind interpretation.