We extend results first announced by Franz et al. (1998), that identified vA 351 = H346 in the Hyades as a multiple star system containing a white dwarf. With Hubble Space Telescope Fine Guidance Sensor fringe tracking and scanning, and more recent speckle observations, all spanning 20.7 years, we establish a parallax, relative orbit, and mass fraction for two components, with a period, $P=2.70$y and total mass 2.1 Msun. With ground-based radial velocities from the McDonald Observatory Otto Struve 2.1m telescope Sandiford Spectrograph, and Center for Astrophysics Digital Speedometers, spanning 37 years, we find that component B consists of BC, two M dwarf stars orbiting with a very short period (P_ BC=0.749 days), having a mass ratio M_C/M_B=0.95. We confirm that the total mass of the system can only be reconciled with the distance and component photometry by including a fainter, higher mass component. The quadruple system consists of three M dwarfs (A,B,C) and one white dwarf (D). We determine individual M dwarf masses M_A=0.53+/-0.10 Msun, M_B=0.43+/-0.04Msun, and M_C=0.41+/-0.04Msun. The WD mass, 0.54+/-0.04Msun, comes from cooling models, an assumed Hyades age of 670My, and consistency with all previous and derived astrometric, photometric, and RV results. Velocities from H-alpha and He I emission lines confirm the BC period derived from absorption lines, with similar (He I) and higher (H-alpha) velocity amplitudes. We ascribe the larger H-alpha amplitude to emission from a region each component shadows from the other, depending on the line of sight.
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