  We present the discovery of >350 GeV gamma-ray emission from the BL Lacertae
object 1ES 2344+514 with the Whipple Observatory 10m gamma-ray telescope. This
is the third BL Lac object detected at gamma-ray energies above 300 Gev, the
other two being Markarian 421 (Mrk 421) and Mrk501. These three active galactic
nuclei are all X-ray selected and have the lowest known redshifts of any BL Lac
objects currently identified. The evidence for emission derives primarily from
an apparent flare on December 20, 1995 when a 6 sigma excess was detected with
a flux approximately 63% of the very high energy gamma-ray emission from the
Crab Nebula, the standard candle for TeV gamma-ray sources. Excluding the
flare, observations between October 1995 and January 1996 yield a 4 sigma
detection corresponding to 11% of the VHE Crab Nebula flux. Observations
spanning September 1996 to January 1997 failed to yield a significant detection
of a steady flux or any flaring. For this period, the 99.9% confidence level
upper limit is <8% of the Crab Nebula. The low baseline emission level and
variations in nightly and yearly flux of 1ES 22344+514 are the same as the VHE
emission characteristics of Mrk 421 and Mrk 501
