Unsupervised parsing is a difficult task that infants readily perform. Progress has been made on this task using text-based models, but few computational approaches have considered how infants might benefit from acoustic cues. This paper explores the hypothesis that word duration can help with learning syntax. We describe how duration information can be incorporated into an unsupervised Bayesian dependency parser whose only other source of information is the words themselves (without punctuation or parts of speech). Our results, evaluated on both adult-directed and child-directed utterances, show that using word duration can improve parse quality relative to words-only baselines. These results support the idea that acoustic cues provide useful evidence about syntactic structure for language-learning infants, and motivate the use of word duration cues in NLP tasks with speech.