Simultaneous observations of 3C 279 at radio, millimeter, near-infrared, optical, ultraviolet (with IUE) and X-ray (with ROSAT) wavelengths were obtained in 1992 December-1993 January, during a three week pointing at the source by the Compton Gamma Ray Observatory. The blazar was in a quiescent or 'low' state during this period. Comparing the multiwavelength energy distribution to that from 1991 June, when 3C 279 was in its brightest recorded gamma-ray state, we find the following: (1) 3C 279 faded dramatically at all frequencies above 10(exp 14) Hz, while the flux variations at low frequencies (radio to millimeter wavelengths) were minor. (2) The near-infrared-optical-ultraviolet spectral shape was softer (steeper) in the quiescent state, and the X-ray spectra also appear softer, although the spectral indix measured by ROSAT refer to a lower energy band than that measured earlier with Ginga. (3) The ratio of the gamma-ray luminosity to that across all other frequencies decreased from a value of approximately equal to 10 in the flaring state to a value approximately equal to 1 in the quiescent state. These findings imply that the production of gamma-rays is closely related to the optical-ultraviolet continuum, in agreement with models where gamma-rays are produced through inverse Compton (IC) scattering by relativistic electrons emitting the synchrotron continuum. The observed nonlinear relation between the synchrotron and IC requires both a change in the electron spectrum and an associated change in the seed photons.