Placocystites forbesianus de Koninck, from the Silurian Dudley Limestone, near Dudley, West Midlands, is here interpreted as a primitive chordate with a calcite skeleton of echinoderm type. This agrees with earlier papers by the senior author and disagrees with the work of Ubaghs (1968 etc.). Applying Hennig's terminology, Placocystites probably belongs to the stem group of the vertebrates and therefore throws light on primitive vertebrate anatomy. It also belongs to the group Calcichordata, set up by one of us as a subphylum (Jefferies 1967). The Calcichordata, however, are not comparable in phylogenetic position with the living chordate subphyla, so the word calcichordate will henceforth be used only informally, for any chordate with a skeleton of echinoderm type. Ubaghs, who has developed a totally different interpretation, assigns Placocystites to the subphylum Homalozoa of the phylum Echinodermata. In assigning it to that phylum, Ubaghs's work is more traditional than ours. Within the calcichordates, Placocystites forbesianus belongs to the more advanced group known as mitrates. These are distinguished from more primitive calcichordates (cornutes) by having right gill slits in addition to left ones. Within the mitrates it is possible to suggest the stem groups, in the Hennigian sense, of acraniates, tunicates and vertebrates. The term standard vertebrate is proposed to denote vertebrates in the usual sense, as contrasted with those stem vertebrates included in the mitrates. The two obvious parts of a calcichordate, formerly called theca and stem, or body and tail, are best called head and tail by homology with standard vertebrates. Mitrates correspond to the tunicate-tadpole-like protovertebrate of 'antisegmentationist' morphologists such as Froriep, Starck and Romer. The uniformly segmented protovertebrate of 'segmentationist' morphologists such as Goodrich would represent a real but later stage in the ancestry of standard vertebrates, descended from a mitrate. The somites of standard vertebrates and acraniates can be plausibly identified inside calcichordates. The premandibular and mandibular somites would be located in the head, along with the buccal cavity, pharynx, gill slits and viscera. The left and right mandibular somites were probably represented in mitrates by the left and right anterior coeloms. The paired premandibular somites would be represented by a crescentic body situated in the posterior part of the head just in front of the brain. The hyoidean somites would be the most anterior pair of somites of the tail, totally separated from gill slits and gill bars. More posterior somites would also be in the tail, behind the hyoidean somites. The homologues of the paired eyes of standard vertebrates can also be recognized as having existed in mitrates (cispharyngeal eyes). The presumed premandibular, mandibular and hyoidean somites were grouped round them in an arrangement which could give rise to the extrinsic eye muscles of standard vertebrates. The ears of mitrates were lateral to the hyoidean somites as they are in living vertebrate embryos. The nervous system of Placocystites and its relatives is comparable with that of a fish. The brain was divided into two parts broadly corresponding to the prosencephalon and rhombencephalon of an early standard vertebrate (though the rhombencephalon of vertebrates also includes derivatives of the mitrate tail). The cranial nerves are deduced to have included olfactory, perhaps terminalis, optic, trigeminal and acusticolateralis complexes. The trigeminal complex included opthalmicus superficialis and ophthalmicus profundus branches and a single pair of ganglia. Contrary to classical theory, it was not divided into profundus and 'true' trigeminal subcomplexes. The pharynx of Placocystites and related mitrates was like that of a tunicate, particularly in certain asymmetries. Details of the skeleton strongly indicate that the pharynx in life would have contained an endostylar mucous trap of tunicate or ammocoete type, as classical theory would predict. The neural gland ('hypophysis') seems to have had the same relations as in a fully formed tunicate tadpole, but was probably endodermal in origin, homologous with Seessel's pouch of a vertebrate. The anatomy of the head of the primitive calcichordate Cothurnocystis, which was a cornute, and like other cornutes and larval amphioxus had left gill slits only, is reconstructed by working backwards from mitrates and by direct evidence from its skeleton. The hypothetical latest common ancestor of lampreys and gnathostomes is deduced. The parts derived from the mitrate head can be distinguished from those derived from the mitrate tail. The animal probably possessed a notochordal head region and a trunk. These would have formed when gill slits and visccra migrated backwards ventral to the anterior part of the mitrate tail. The pericardium would have arisen by ventral growth of mitrate tail somites down the gill bars and their fusion ventrally to form a cavity. The visceral coelom arose by the ventral growth of mitrate tail somites round the viscera, accompanied by the development and fusion of cavities in the ventral parts of these somites. The branchial nerves of standard vertebrates are a mixture of placodal elements, probably derived from the mitrate head, and neural crest elements, probably derived from the mitrate tail. This hypothetical animal probably evolved from the mitrates when one of them took to habitual forwards swimming. Placocystites probably crept backwards through the sediment just below the sea bottom, pulled by the tail. A pair of spines near the mouth would serve to cut into the sediment, probably assisted by water squirted along them from the buccal cavity.