  The BL Lacertae (BL Lac) object 1ES 2344+514 (1ES 2344), at a redshift of
0.044, was discovered as a source of very high energy (VHE) gamma rays by the
Whipple Collaboration in 1995 \citep{2344Catanese98}. This detection was
recently confirmed by the HEGRA Collaboration \citep{2344Hegra03}. As is
typical for high-frequency peaked blazars, the VHE gamma-ray emission is highly
variable. On the night of 20 December, 1995, a gamma-ray flare of 5.3-sigma
significance was detected, the brightest outburst from this object to-date. The
emission region is compatible with a point source. The spectrum between 0.8 TeV
and 12.6 TeV can be described by a power law $\frac{\ud^3 N}{\ud E \ud A \ud
t}=(5.1\pm1.0_{st}\pm1.2_{sy})\times10^{-7} (E/ \mathrm{TeV})^{-2.54
\pm0.17_{st}\pm0.07_{sy}} \mathrm{\frac{1}{TeV m^2 s}}$. Comparing the spectral
index with that of the other five confirmed TeV blazars, the spectrum of 1ES
2344 is similar to 1ES 1959+650, located at almost the same distance. The
spectrum of 1ES 2344 is steeper than the brightest flare spectra of Markarian
421 (Mrk~421) and Markarian 501 (Mrk~501), both located at a distance about 2/3
that of 1ES 2344, and harder than the spectra of PKS 2155-304 and H~1426+428,
which are located almost three times as far. This trend is consistent with
attenuation caused by the infrared extragalactic background radiation.
