Lagynocystis pyramidalis (Barrande) from the marine Lower Ordovician of Bohemia (Sarka Formation (Llanvirn)), has features which suggest that it is ancestral, or nearly so, to living cephalochordates such as amphioxus (Branchiostoma). L. pyramidalis belongs to a strange group of fossils classified by some workers as 'carpoid' echinoderms (phylum Echinodermata, subphylum Homalozoa, class Stylophora). They are better seen, however, as primitive chordates with echinoderm affinities (phylum Chordata, subphylum Calcichordata Jefferies, 1967, class Stylophora). The most striking echinoderm-like feature of the calcichordates is their calcite skeleton with each plate a single crystal of calcite. Their chordate characters include: (1) branchial slits; (2) a postanal tail (stem) with muscle blocks, notochord, dorsal nerve cord and segmental ganglia; (3) a brain and cranial nervous system like those of a fish; and (4) various asymmetries like those of recent primitive chordates. The calcichordates are divided into a more primitive order, Cornuta, and a more advanced order Mitrata, which evolved from Cornuta. L. pyramidalis is a specialized member of the order Mitrata. Forms up till now associated with it in the suborder Lagynocystida of the Mitrata are better separated from it to form a new suborder Peltocystida (Kirkocystidae plus Peltocystidae). The features which ally L. pyramidalis to amphioxus are as follows: (1) a median ventral atrium opening by a median ventral atriopore; (2) a probably excretory posterior coelom which could give rise to the nephridia of amphioxus by upward growth of the gill slits; (3) evidence that the anus opened externally on the left; (4) evidence that the mouth and buccal cavity was innervated more strongly from the left than from the right; (5) evidence suggesting that, if it swam, L. pyramidalis would rotate about its long axis, clockwise as seen from behind, like late larval amphioxus and larval tunicates. The amphioxus-like features of L. pyramidalis are imposed on the pattern of a very primitive mitrate. There existed thus: (1) a well-developed brain and the cranial nerves were more of the vertebrate pattern than those of amphioxus; (2) left and right branchial openings in addition to the median atriopore; and (3) the tail or stem had paired segmental ganglia. The latest common ancestor of vertebrates and amphioxus would be a primitive mitrate. It follows, since Lagynocystis had a calcite skeleton, that such a skeleton has been lost at least twice in the evolution of the chordates.