We present the results of six BeppoSAX observations of 1ES 2344+514, five o
f which were taken within one week. 1ES 2344+514, one of the few known TeV
BL Lac objects, was detected by the BeppoSAX Narrow Field Instruments (NFI)
in the range 0.1 and approximate to 50 keV. During the first five closely
spaced observations 1ES 2344+514 showed large-amplitude luminosity variabil
ity, associated with spectacular spectral changes: in particular, the last
observation found the source to be several times fainter, with a much steep
er X-ray spectrum. The energy-dependent shape of the light curve and the sp
ectral changes both imply a large frequency shift (by a factor of 30 or mor
e) of the peak of synchrotron emission. At maximum flux the peak was locate
d at, or above, 10 keV, making 1ES 2344+514 the second blazar (after Mrk 50
1) to have a synchrotron peak in the hard X-ray band. The frequency shift,
and the corresponding increase in luminosity, might be caused by 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 time-scale
of approximately 5000 s has also been detected when the source was brighte
st.