The grammar, or syntax, of human language is typically understood in terms of abstract hierarchical structures. However, theories of language processing that emphasize sequential information, not hierarchy, successfully model diverse phenomena. Recent work probing brain signals has shown mixed evidence for hierarchical information in some tasks. We ask whether sequential or hierarchical information guides the expectations that a human listener forms about a word’s part-of-speech when simply listening to every-day language. We compare the predictions of three computational models against electroencephalography signals recorded from human participants who listen passively to an audiobook story. We find that predictions based on hierarchical structure correlate with the human brain response above-and-beyond predictions based only on sequential information. This establishes a link between hierarchical linguistic structure and neural signals that generalizes across the range of syntactic structures found in every-day language.