We present new X-ray observations of the nearby Herbig Ae star HD 104237 (= DX Cha) with XMM-Newton, whose objective is to clarify the origin of the emission. Several X-ray emission lines are clearly visible in the CCD spectra, including the high-temperature Fe K-alpha complex. The emission can be accurately modeled as a multi-temperature thermal plasma with cool (kT < 1 keV) and hot (kT > 3 keV) components. The presence of a hot component is compelling evidence that the X-rays originate in magnetically confined plasma, either in the Herbig star itself or in the corona of an as yet unseen late-type companion. The X-ray temperatures and luminosity (log Lx = 30.5 ergs/s) are within the range expected for a T Tauri companion, but high resolution Chandra and HST images constrain the separation of a putative companion to less than 1 arcsec. We place these new results into broader context by comparing the X-ray and bolometric luminosities of a sample of nearby Herbig stars with those of T Tauri stars and classical main-sequence Be stars. We also test the predictions of a model that attributes the X-ray emission of Herbig stars to magnetic activity that is sustained by a shear-powered dynamo.