The bryozoan family Chlidoniopsidae Harmer, 1957 is reviewed in relation to a new Paleogene European fossil, Celiopsis vici new genus and new species. It differs from the type and only other genus of the family in having longer internodes with up to three zooids, shorter proximal caudae, and, more importantly, suture lines that unequally divided the umbonuloid frontal shield and basal (abfrontal) wall (and the hypostegal coelom in life) into sectors, analogous to the situation in the lepralioid-shielded Prostomariidae and Urceoliporidae. Unlike Prostomaria and Urceolipora, and like Chlidoniopsis, Celiopsis is uniserial. The suture lines in Celiopsis were lines of insertion (attachment) of epithecal membranes in life and each sector has its own longitudinal series of septular pores, sometimes doubled. Miocene to Recent Chlidoniopsis contains two species, and Eocene–Oligocene Celiopsis contains three species. The geographic distribution gives evidence of origination of the family in the Paratethys of Europe, with southeastwards migration to Australia and the tropical western Pacific. The temporal distribution suggests two macro-evolutionary trends—from multizooidal to unizooidal internodes, and from a broader area of basal wall, with a division into separate cryptocystal fields, to a narrower basal wall with no such division.