The rings of Uranus are oriented edge-on to Earth in 2007 for the first time since their 1977 discovery. This event provides a rare opportunity to observe their dark (unlit) side, where dense rings darken to near invisibility, but faint rings become much brighter. We present a ground-based infrared image of the unlit side of the rings that shows that the system has changed dramatically since previous views. A broad cloud of faint material permeates the system but is not correlated with the well-known narrow rings or with the embedded dust belts imaged by the Voyager spacecraft. Although some differences can be explained by the unusual viewing angle, we conclude that the dust distribution within the system has changed substantially since the 1986 Voyager encounter and that it occurs on much larger scales than has been seen in other planetary systems.