New species of ostracods are described from the Tremadoc of the Cordillera Oriental (Argentina). These are among the earliest well-documented records of Ostracoda sensu stricto. The ostracod assemblages are sourced from shallow marine clastics and are dominated by palaeocopes (Eopilla waisfeldae n. sp., Nanopsis coquena n. sp.), and the binodicope Kimsella luciae n. gen. and sp. Eopilla and Kimsella show affinities with species from paleocontinental Gondwana (e.g., Ibero-Armorica, Turkey, Australia, Carnic Alps), but Nanopsis is previously known only from paleocontinental Baltica. This study confirms that two of the major clades of Ordovician ostracods, namely the Binodicopa and the Palaeocopa, were already geographically widespread during the late Tremadoc, suggesting a still earlier origin for these groups, possibly from within the Cambrian to Early Ordovician Bradoriida. Evidence from soft-part anatomy indicates that phosphatocopids, the other group hypothesized to be ancestral ostracods, have apomorphies that preclude them as direct ancestors. The origin of ostracods is more likely to be found within the Bradoriida, a probable polyphyletic group that resembles Early Ordovician ostracods in the external sculpture of their bivalved carapace. Evidence from carapace morphology suggests that the ancestors of true ostracods might lie within the bradoriid groups Beyrichonidae and Hipponicharionidae, a hypothesis that can only truly be tested when more evidence from fossilized soft tissues becomes available.