The close X-ray-selected BL Lac PKS 2155-304 has been observed using the Un
iversity of Durham Mark 6 very high energy (VHE) gamma-ray telescope during
1996 September/October/November and 1997 October/November, VHE gamma rays
with energy more than 300 GeV were detected from this object with a time-av
eraged integral flux of (4.2 +/- 0.7(stat) +/- 2.0(sys)) x 10(-11) cm(-2) s
(-1). There is evidence for VHE gamma-ray emission during our observations
in 1996 September and 1997 October/November, with the strongest emission be
ing detected in 1997 November, when the object was producing the largest fl
ux ever recorded in high-energy X-rays and it was detected as a source of g
amma rays of energy greater than 100 MeV. The VHE and X-ray fluxes show evi
dence of a correlation.