The tricranocladine sponges (now assigned to the suborder Eutaxicladina) are a conservative group consisting of the single family Hindiidae. The genus Hindia Duncan is considered the base of the tricranoclad evolutionary record. A new sponge discovered from the Ordovician limestones of the San Juan Formation in the Argentine Precordillera allows a reexamination of the Hindiid lineage and extends the early history of the tricranocladines back to the Darriwilian. Eoscheiella concava n. gen. and sp. is described and illustrated. It is known from a single chertified, spherical specimen with a central hollow core, a typical character found in several genera of the family. Tricranoclads, megarhizoclones, and radial monaxonic spicules are the main skeletal components of the new genus. The presence of a band of subparalell tangential monaxons on the surface of Eoscheiella can be related to an inferred, small, root tuft that attached the spherical sponge to the substrate. The discovery of Eoscheiella modifies the evolutionary view of the family, for it is the oldest genus now known with simple dipodal and tripodal tricranoclads without a brachyome, radial monaxons, and megarhizoclones. Eoscheiella displaces the genus Hindia from the base of tricranocladine evolutionary history. Variability in spicule form, arrangement, and clasping possibilities observed in Permian representatives are clearly more accentuated in the Ordovician Eoscheiella. All these features appeared earlier than expected in previously proposed evolutionary trends.