Mrk 421 was observed for about 2 days with BeppoSAX in 1998 April as part o
f a worldwide multiwavelength campaign. A large, well-defined flare was obs
erved in X-rays. The same flare was observed simultaneously at TeV energies
by the Whipple Observatory gamma-ray telescope. These data provide (1) the
first evidence that the X-ray and TeV intensities are well correlated on t
imescales of hours and (2) the first exactly simultaneous X-ray and TeV spe
ctra. The results imply that the X-ray and TeV photons derive from the same
region and from the same population of relativistic electrons. 'The physic
al parameters deduced from a homogeneous synchrotron self-Compton model for
the spectral energy distribution yield electron cooling times close to the
observed variability timescales.