  We present the results of six BeppoSAX observations of 1ES 2344+514, five of
which were taken within a week. 1ES 2344+514, one of the few known TeV BL Lac
objects, was detected by the BeppoSAX Narrow Field Instruments between 0.1 to
\~50 keV. During the first five closely spaced observations 1ES 2344+514 showed
large amplitude luminosity variability, associated with spectacular spectral
changes, particularly when compared to the last observation when the source was
found to be several times fainter, with a much steeper X-ray spectrum. The
energy dependent shape of the lightcurve and the spectral changes imply a large
shift (factor of 30 or more in frequency) of the peak of the synchrotron
emission. At maximum flux the peak was located at or above 10 keV, making 1ES
2344+514 the second blazar (after MKN501) with the synchrotron peak in the hard
X-ray band. The shift, and the corresponding increase in luminosity, might be
due to the onset of a second synchrotron component extending from the soft to
the hard X-ray band where most of the power is emitted. Rapid variability on a
timescale of approximately 5000 seconds has also been detected when the source
was brightest.
