We present multiwavelength observations of the BL Lacertae object Markarian 501 (Mrk 501) in 1997 between April 8 and April 19. Evidence of correlated variability is seen in very high energy (VHE; E gsim 350 GeV) γ-ray observations taken with the Whipple Observatory γ-ray telescope, data from the Oriented Scintillation Spectrometer Experiment of the Compton Gamma Ray Observatory, and quick-look results from the All-Sky Monitor of the Rossi X-Ray Timing Explorer, while EGRET did not detect Mrk 501. Short-term optical correlations are not conclusive, but the U-band flux observed with the 1.2 m telescope of the Whipple Observatory was 10% higher than in March. The average energy output of Mrk 501 appears to peak in the 2-100 keV range, which suggests an extension of the synchrotron emission to at least 100 keV, the highest observed in a blazar and ~100 times higher than that seen in the other TeV-emitting BL Lac object, Mrk 421. The VHE γ-ray flux observed during this period is the highest ever detected from this object. The VHE γ-ray energy output is somewhat lower than the 2-100 keV range, but the variability amplitude is larger. The correlations seen here do not require relativistic beaming of the emission unless the VHE spectrum extends to gsim5 TeV.