Evidence for TeV gamma ray emission from Cassiopeia A

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 +/- 1.2_stat +/- 1.2_syst) 10^-9 ph m^-2 s^-1 above 1 TeV was derived. The spectral distribution is consistent with a power law with a differential spectral index of -2.5 +/- 0.4_stat +/- 0.1_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.