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 $frac{ud^3 N}{ud E ud A ud t}=(5.1pm1.0_{st}pm1.2_{sy})times10^{-7} (E/ mathrm{TeV})^{-2.54 pm0.17_{st}pm0.07_{sy}} mathrm{frac{1}{TeV m^2 s}}$. 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.
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