To understand the nature of transient obscuring outflows in active galactic nuclei, we observed the Seyfert 1 galaxy NGC 3783 on two occasions in December 2016 triggered by Swift monitoring indicating strong soft X-ray absorption in November. We obtained ultraviolet spectra using COS on HST and optical spectra using FEROS on the MPG/ESO 2.2-m telescope that were simultaneous with X-ray spectra from XMM-Newton and NuSTAR. We find new components of broad, blue-shifted absorption associated with Ly$alpha$, ion{N}{v}, ion{Si}{iv}, and ion{C}{iv} in our COS spectra. The absorption extends from velocities near zero in the rest-frame of the host galaxy to $-6200$ $rm km~s^{-1}$. These features appear for the first time in NGC 3783 at the same time as the heavy soft X-ray absorption seen in the XMM-Newton X-ray spectra. The X-ray absorption has a column density of $sim 10^{23}~rm cm^{-2}$, and it partially covers the X-ray continuum source. The X-ray absorption becomes more transparent in the second observation, as does the UV absorption. Combining the X-ray column densities with the UV spectral observations yields an ionization parameter for the obscuring gas of log $xi =1.84^{+0.4}_{-0.2}$ $rm erg~cm~s^{-1}$. Despite the high intensity of the UV continuum in NGC 3783, F(1470 AA)=$8 times 10^{-14}~rm erg~cm^{-2}~s^{-1}~AA^{-1}$, the well known narrow UV absorption lines are deeper than in earlier observations in unobscured states, and low ionization species such as ion{C}{iii} appear, indicating that the narrow-line gas is more distant from the nucleus and is being shadowed by the gas producing the obscuration. Despite the high continuum flux levels in our observations of NGC 3783, moderate velocities in the UV broad line profiles have substantially diminished. We suggest that a collapse of the broad line region has led to the outburst and triggered the obscuring event.