Infants are precocious word learners, and seem to possess systematic expectations about how words refer to object kinds. For example, while monolingual infants show a one‐to‐one mapping bias (e.g. mutual exclusivity), expecting each object to have only one basic level label, previous research has shown that this is less robust in bi‐ and multilinguals aged 1.5 years and older. This study examined the early origins of such one‐to‐one mapping biases by comparing monolingual and bilingual 9–10‐month‐olds’ expectations about the relationship between labels and object kinds. In a violation of expectation paradigm, infants heard a speaker name hidden objects with either one label (‘I see a mouba! I see a mouba!’) or two labels (‘I see a camo! I see a tenda!’). An occluder moved to reveal two objects that were either identical or of different kinds. Monolingual infants looked longest when two labels were associated with identical objects, and when one label was associated with objects of different kinds, showing that they found these outcomes unexpected. This replicated previous findings showing that monolinguals expect that distinct words label distinct object kinds (Dewar & Xu, ). Bilinguals looked equally to the outcomes regardless of the number of labels, showing no such expectations. This finding indicates that bilingualism influences young infants’ expectations about how words refer to kinds, and more broadly supports the position that language experience contributes to the development of word learning heuristics. In a violation‐of‐expectation study, 9‐month‐old monolingual infants expected a one‐to‐one relationship between labels and object kinds, but bilingual infants did not. Language experience affects the development of word learning heuristics even before children have acquired a sizeable vocabulary.