We present evidence for shock acceleration of cosmic rays to high energies ( \sim 10 TeV ) in the supernova remnant IC 443 . X-ray imaging spectroscopy with ASCA reveals two regions of particularly hard emission : an unresolved source embedded in an extended emission region , and a ridge of emission coincident with the southeastern rim . Both features are located on part of the radio shell where the shock wave is interacting with molecular gas , and together they account for a majority of the emission at 7 keV . Though we would not have noticed it a priori , the unresolved feature is coincident with one resolved by the ROSAT HRI . Because this feature overlaps a unique region of flat radio spectral index ( \alpha < 0.24 ) , has about equal light-crossing and synchrotron loss times , and a power law spectrum with a spectral index of \alpha =1.3 \pm 0.2 , we conclude that the hard X-ray feature is synchrotron radiation from a site of enhanced particle acceleration . Evidence against a plerion includes a lack of observed periodicity ( the pulsed fraction upper limit is 33 % ) , the spectral similarity with the more extended hard region , the location of the source outside the 95 % error circle of the nearby EGRET source , the fact that it is nestled in a bend in the molecular cloud ring with which IC 443 is interacting , and the requirement of an extremely high transverse velocity ( \geq 5,000 km/s ) . We conclude that the anomalous feature is most likely tracing enhanced particle acceleration by shocks that are formed as the supernova blast wave impacts the ring of molecular clouds .