The chordates, hemichordates (such as acorn worms) and echinoderms (such as starfish) comprise the group Deuterostomia, well established as monophyletic. Among extant deuterostomes, a skeleton in which each plate has the crystallographic structure of a single crystal of calcite is characteristic of echinoderms and is always associated with radial symmetry and never with gill slits. Among fossils, however, such a skeleton sometimes occurs without radial symmetry. This is true of Jaekelocarpus oklahomensis, from the Upper Carboniferous of Oklahoma, USA, which, being externally almost bilaterally symmetrical, is traditionally placed in the group Mitrata (Ordovician to Carboniferous periods, 530-280 million years ago), by contrast with the bizarrely asymmetrical Cornuta (Cambrian to Ordovician periods, 540 to 440 million years ago). Using computer X-ray microtomography, we describe the anatomy of Jaekelocarpus in greater detail than formerly possible, reveal evidence of paired gill slits internally and interpret its functional anatomy. On this basis we suggest its phylogenetic position within the deuterostomes.