The evolutionary origin of feathers has long been obscured because no morphological antecedents were known to the earliest, structurally modern feathers of Archaeopteryx. It has been proposed that the filamentous integumental appendages on several theropod dinosaurs are primitive feathers; but the homology between these filamentous structures and feathers has been disputed, and two taxa with true feathers (Caudipteryx and Protarchaeopteryx) have been proposed to be flightless birds. Confirmation of the theropod origin of feathers requires documentation of unambiguously feather-like structures in a clearly non-avian theropod. Here we describe our observations of the filamentous integumental appendages of the basal dromaeosaurid dinosaur Sinornithosaurus millenii, which indicate that they are compound structures composed of multiple filaments. Furthermore, these appendages exhibit two types of branching structure that are unique to avian feathers: filaments joined in a basal tuft, and filaments joined at their bases in series along a central filament. Combined with the independent phylogenetic evidence supporting the theropod ancestry of birds, these observations strongly corroborate the hypothesis that the integumental appendages of Sinornithosaurus are homologous with avian feathers. The plesiomorphic feathers of Sinornithosaurus also conform to the predictions of an independent, developmental model of the evolutionary origin of feathers.