A detection of TeV gamma-rays from Mkn 501 is reported, based on obser
vations made between March and August 1996 with the first HEGRA Cheren
kov telescope (CT1). From the image analysis, 351 excess candidate gam
ma-ray events are obtained from the 147 h dataset. The statistical sig
nificance of the excess is 5.2 sigma. The average excess rate is 2.4 /- 0.5 h(-1) above the approximate to 1.5 TeV threshold of CT1. Under
the assumption that the spectrum of Mkn 501 follows a power law we fin
d a differential spectral index of 2.6 +/- 0.5 and obtain a time-avera
ged integral flux above 1.5 TeV of 2.3(+/-0.4)(Stat)(+1.5 - 0.6)(Syst)
x 10(-12) cm(-2) s(-1). Comparison with our near contemporary observa
tions of the Crab Nebula, used as a standard candle to test CT1 after
upgrading to a 127 pixel camera, indicates that Mkn 501 has a spectrum
similar to that of the Crab Nebula above 1.5 TeV. The integral flux a
bove 1.5 TeV from Mkn 501 is found to have been between 2.2 and 3.6 ti
mes smaller than that from the Crab Nebula. HEGRA is the second experi
ment to have detected Mkn 501 in the TeV range.