A large incomplete rodent femur from a Quaternary cave deposit near Barahona, Puerto Rico, is established as the holotype of Tainotherium valei, a new extinct genus and species. Although biogeographic and body size similarities suggest that it may be related to the Puerto Rican giant hutia Elasmodontomys, the Antillean large-bodied rodent family Heptaxodontidae is now interpreted as invalid, and it is impossible to assign Tainotherium to a particular caviomorph family in the absence of associated craniodental material. Tainotherium differs from other West Indian species in possessing a large femoral head, a proximally angled femoral neck, a short greater trochanter and a medially positioned lesser trochanter unconnected by an intertrochanteric crest, and a transversely flattened, anteroposteriorly bowed shaft lacking well-defined ridges. These characters are all associated with arboreal life habits in other mammal groups. The Puerto Rican land mammal fauna was dominated by a rodent radiation occupying a wide variety of niches before human arrival in the West Indies, but although arboreality is correlated with increased likelihood of survival in Quaternary mammalian extinction events, all of this fauna is now extinct. It is unlikely that decreasing aridity and the reduction of Puerto Rican savanna-type environments at the end of the Pleistocene contributed to the extinction of the arboreal Tainotherium, and habitat destruction by pre-Columbian Amerindians may instead have been responsible.