We present the 2–60 keV spectrum of the supernova remnant Cassiopeia A measured using the Proportional Counter Array and the High Energy X-ray Timing Experiment on the Rossi X-ray Timing Explorer satellite . In addition to the previously reported strong emission-line features produced by thermal plasmas , the broad-band spectrum has a high-energy “ tail ” that extends to energies at least as high as 120 keV . This tail may be described by a broken power law that has photon indices of \Gamma _ { 1 } = 1.8 ^ { +0.5 } _ { -0.6 } and \Gamma _ { 2 } = 3.04 ^ { +0.15 } _ { -0.13 } and a break energy of E _ { b } = 15.9 ^ { +0.3 } _ { -0.4 } keV . We argue that the high-energy component , which dominates the spectrum above about 10 keV , is produced by synchrotron radiation from electrons that have energies up to at least 40 TeV . This conclusion supports the hypothesis that Galactic cosmic rays are accelerated predominantly in supernova remnants .