A detection of Gamma-rays from Mkn 421 at energies above 1 TeV is reported, based on observations made in December 1994 - May 1995 with the first two HEGRA Cherenkov telescopes. >From the image analysis, 111 excess gamma candidates are obtained from the 26 h Telescope #1 (CT1) dataset (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 detection 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 contemporary observations of the Crab Nebula indicates that Mkn 421 has a steeper spectrum than the Crab Nebula above 1 TeV. Under the assumption that the spectrum of Mkn 421 follows a power law, we obtain a differential spectral 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.
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