A left mandible of a new tillodont from the Upper Willwood, Early Eocene of Buffalo Basin, Wyoming, is described. It represents a new genus and species, Megalesthonyx hopsoni. Included as parts of the type specimen are an upper incisor and several bones of the forefeet. Also referred to this species are a lower premolar, an upper premolar and two upper molars. The new specimen is intermediate between Esthonyx and Trogosus in time and in many morphologic characters. Sufficient evidence is lacking to prove that Megalesthonyx was ancestral to Trogosus, but most features now known suggest that it was. The transitional state of this form supports the recognition of a single family, Esthonychidae, for these strange mammals. Two subfamilies are observed. The Tillodontia are regarded as a distinct order, contra Van Valen (1963), on the basis of extreme dental specializations.