A detection of gamma-rays from Mkn 421 at energies above 1 TeV is repo
rted, based on observations made in December 1994 - May 1995 with the
first two HEGRA Cherenkov telescopes. From the image analysis, 111 exc
ess gamma candidates are obtained from the 26 h Telescope #1 (CT1) dat
aset (significance 4.0 sigma) and 218 from the 41 h Telescope #2 (CT2)
dataset (significance 4.2 sigma) at zenith angles theta < 25 degrees.
The combined significance is approx. 5.8 sigma. This is the second de
tection of Mkn 421 at TeV energies. The average excess rate is 4.3 +/-
1.0 h(-1) for CT1 and 5.4+/-1.3 h(-1) for CT2. Comparison with our co
ntemporary observations of the Crab Nebula indicates that Mkn 421 has
a steeper spectrum than the Crab Nebula above 1 TeV. Under the assumpt
ion that the spectrum of Mkn 421 follows a power law, we obtain a diff
erential spect ral index of 3.6+/-1.0 and an integral flux above 1 TeV
of 8(+/-2)(Stat)(+6-3)(Syst) x 10(-12) cm(-2)s(-1) from a comparison
with Monte Carlo data. This flux is smaller than the Crab Nebula flux
by a factor of 2.0+/-0.8.