Hyperion, Saturn's eighth largest icy satellite, is a body of irregular shape in a state of chaotic rotation. The surface is segregated into two distinct units. A spatially dominant high-albedo unit having the strong signature of H2O ice contrasts with a unit that is about a factor of four lower in albedo and is found mostly in the bottoms of cup-like craters. Here we report observations of Hyperion's surface in the ultraviolet and near-infrared spectral regions with two optical remote sensing instruments on the Cassini spacecraft at closest approach during a fly-by on 25-26 September 2005. The close fly-by afforded us the opportunity to obtain separate reflectance spectra of the high- and low-albedo surface components. The low-albedo material has spectral similarities and compositional signatures that link it with the surface of Phoebe and a hemisphere-wide superficial coating on Iapetus.