Early coelomic development in the abbreviated development of the sea urchin Holopneustes purpurescens is described and then used in a comparison with coelomic development in chordate embryos to support homology between a single arm of the five-armed radial body plan of an echinoderm and the single bilateral axis of a chordate. The homology depends on a positional similarity between the origin of the hydrocoele in echinoderm development and the origin of the notochord in chordate development, and a positional similarity between the respective origins of the coelomic mesoderm and chordate mesoderm in echinoderm and chordate development. The hydrocoele is homologous with the notochord and the secondary podia are homologous with the somites. The homology between a single echinoderm arm and the chordate axis becomes clear when the aboral to oral growth from the archenteron in the echinoderm larva is turned anteriorly, more in line with the anterior-posterior axis of the early zygote. A dorsoventral axis inversion in chordates is not required in the proposed homology.