232 hours of data were accumulated from 1997 to 1999 , using the HEGRA Stereoscopic Cherenkov Telescope System to observe the supernova remnant Cassiopeia A. TeV \gamma -ray emission was detected at the 5 \sigma level , and a flux of ( 5.8 \pm 1.2 _ { \mathrm { stat } } \pm 1.2 _ { \mathrm { syst } } ) \times 10 ^ { -9 } \mbox { ph } % \mbox { m } ^ { -2 } \mbox { s } ^ { -1 } above 1 TeV was derived . The spectral distribution is consistent with a power law with a differential spectral index of -2.5 \pm 0.4 _ { \mathrm { stat } } \pm 0.1 _ { \mathrm { syst } } between 1 and 10 TeV . As this is the first report of the detection of a TeV \gamma -ray source on the “ centi-Crab ” scale , we present the analysis in some detail . Implications for the acceleration of cosmic rays depend on the details of the source modeling . We discuss some important aspects in this paper .