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 (Catanese et al.). This detection was recently confirmed by the HEGRA collaboration (Tluczykont et al.). As is typical for high-frequency-peaked blazars, the VHE gamma-ray emission is highly variable. On the night of 1995 December 20, a gamma-ray flare of 5.3 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 and 12.6 TeV can be described by a power law, If we compare the spectral index with that of the other five confirmed TeV blazars, the spectrum of 1ES 2344 is similar to that of 1ES 1959+650, which is 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 of which are located at a distance about two-thirds that of 1ES 2344, and harder than the spectra of PKS 2155À304 and H1426+428, which are located almost 3 times as far away. This trend is consistent with attenuation caused by the infrared extragalactic background radiation.