The modern sperm whales Kogia and Physeter (superfamily Physeteroidea) represent highly disparate, relict members of a group of odontocetes that peaked in diversity during the middle to late Miocene. Based on a highly informative specimen (including the cranium with ear bones, mandibles, teeth and some postcranial elements) from the lower Miocene (early Burdigalian, 19–18 Ma) of the Chilcatay Formation (Pisco Basin, Peru), we describe here a new genus and species of physeteroid, Rhaphicetus valenciae gen. et sp. nov. The latter is one of the geologically oldest physeteroids. This medium-sized species (estimated body length between 4.7 and 5.7 m) differs from all other physeteroids by the following, probably autapomorphic, features: a narrow, cylindrical rostrum comprising nearly 75% of the condylobasal length; the two main dorsal infraorbital foramina located posterior to the antorbital notch; an upper tooth count of at least 36 teeth per quadrant; and anterior-most upper alveoli filled by thick bony pads. Our phylogenetic analysis recovers R. valenciae as one of the earliest branching stem physeteroids. The highly unusual filling of the anterior upper alveoli by bony pads is interpreted as part of a mechanism leading to the loss of apical and subapical upper teeth. By comparison with other odontocetes displaying some degree of anterior reduction of the dentition, this condition may have corresponded to the rostrum being anteriorly longer than the mandible. The elongated rostrum with a circular cross-section, the long temporal fossa, and the high number of slender, pointed upper and lower teeth all suggest that R. valenciae used its dentition to grasp relatively small prey, possibly via rapid movements of the head. On the one hand, this new Peruvian record increases our knowledge of the morphological disparity of sperm whales during the Miocene. On the other hand, it may provide clues to the ancestral morphotype for all physeteroids. http://zoobank.org/urn:lsid:zoobank.org:pub:3E1CEFC8-0F23-416E-9C02-03750D7199BA.