We present the results of recent Chandra High-Energy Transmission Grating Spectrometer and Hubble Space Telescope Cosmic Origins Spectrograph observations of the nearby Seyfert 1 galaxy NGC 3783 which shows a strong , non-varying X-ray warm absorber and physically related and kinematically varying UV absorption . We compare our new observations to high-resolution , high signal-to-noise archival data from 2001 , allowing a unique investigation into the long-term variations of the absorption over a 12 yr period . We find no statistically significant changes in the physical properties of the X-ray absorber , but there is a significant drop of \sim 40 \% in the UV and X-ray flux , and a significant flattening of the underlying X-ray power-law slope . Large kinematic changes are seen in the UV absorbers , possibly due to radial deceleration of the material . Similar behavior is not observed in the X-ray data , likely due to its lower velocity resolution , which shows an outflow velocity of v _ { out } \sim - 655 { km s ^ { -1 } } in both epochs . The narrow iron K \alpha emission line at 6.4 keV shows no variation between epochs , and its measured width places the material producing the line at a radial distance of \sim 0.03 pc from the central black hole .