232 hours of data were accumulated from 1997 to 1999, using the HEGRA Stere
oscopic Cherenkov Telescope System to observe the supernova remnant Cassiop
eia A. TeV gamma -ray emission was detected at the 5 sigma level, and a flu
x of (5.8 +/- 1.2(stat) +/- 1.2(syst)) 10(-9) ph m(-2) s(-1) above 1 TeV wa
s 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 a
nd 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 t
he source modeling. Sire discuss some important aspects in this paper.