A key step in the evolutionary history of Odontoceti (echolocating toothed cetaceans) is the transition from the ancestral heterodont condition – characterized by the presence of double-rooted cheek teeth bearing accessory denticles – to the homodont dentition displayed by most extant odontocete species. During the last few decades, new finds and the reassessment of specimens in collections revealed an increased morphological disparity amongst the Oligo–Miocene heterodont odontocetes. Based on a partly articulated skeleton from late Early Miocene (Burdigalian, 18.8–18.0 Ma) beds of the Chilcatay Formation (Pisco Basin, Peru), we describe a new genus and species of heterodont odontocete, Inticetus vertizi, in the new family Inticetidae. This large dolphin is characterized by, amongst other things, a long and robust rostrum bearing at least 18 teeth per quadrant; the absence of procumbent anterior teeth; many large, broad-based accessory denticles in double-rooted posterior cheek teeth; a reduced ornament of dental crowns; the styliform process of the jugal being markedly robust; a large fovea epitubaria on the periotic, with a correspondingly voluminous accessory ossicle of the tympanic bulla; and a shortened tuberculum of the malleus. Phylogenetic analyses (with and without molecular constraint; with and without down-weighting of homoplastic characters) yielded contrasting results, with Inticetus falling either as a stem Odontoceti or as an early branching member of a large Platanistoidea clade. With its large size, robust rostrum and unusual dental morphology, and the absence of conspicuous tooth wear, Inticetus increases the morphological and ecological disparity of Late Oligocene–Early Miocene heterodont odontocetes. Finally, this new taxon calls for caution when attempting to identify isolated cetacean cheek teeth, even at the suborder level. http://zoobank.org/urn:lsid:zoobank.org:pub:5B306B49-EB1B-42F9-B755-B0B05B4F938F.