Mrk 421 was observed for about 2 days with BeppoSAX in 1998 April as part of a worldwide multiwavelength campaign. A large, well-defined flare was observed 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 timescales of hours and (2) the first exactly simultaneous X-ray and TeV spectra. The results imply that the X-ray and TeV photons derive from the same region and from the same population of relativistic electrons. The physical parameters deduced from a homogeneous synchrotron self-Compton model for the spectral energy distribution yield electron cooling times close to the observed variability timescales.