Prosodic information is crucial for spoken language comprehension and especially for syntactic parsing, because prosodic cues guide the hearer's syntactic analysis. The time course and mechanisms of this interplay of prosody and syntax are not yet well understood. In particular, there is an ongoing debate whether local prosodic cues are taken into account automatically or whether they are processed in relation to the global prosodic context in which they appear. The present study explores whether the perception of a prosodic boundary is affected by its position within an utterance. In an event-related potential (ERP) study we tested if the brain response evoked by the prosodic boundary differs when the boundary occurs early in a list of three names connected by conjunctions (i.e., after the first name) as compared to later in the utterance (i.e., after the second name). A closure positive shift (CPS) — marking the perception of a prosodic phrase boundary — was elicited only for stimuli with a late boundary, but not for stimuli with an early boundary. This shows that prosodic information plays an immediate role in language perception, but only when the processing is licensed by contextual, that is, previously processed information.