Teeth and jaws constitute a model of the evolutionary developmental biology concept of modularity and they have been considered the key innovations underpinning a classic example of adaptive radiation. However, their evolutionary origins are much debated. Placoderms comprise an extinct sister clade or grade to the clade containing chondrichthyans and osteichthyans, and although they clearly possess jaws, previous studies have suggested that they lack teeth, that they possess convergently evolved tooth-like structures or that they possess true teeth. Here we use synchrotron radiation X-ray tomographic microscopy (SRXTM) of a developmental series of Compagopiscis croucheri (Arthrodira) to show that placoderm jaws are composed of distinct cartilages and gnathal ossifications in both jaws, and a dermal element in the lower jaw. The gnathal ossification is a composite of distinct teeth that developed in succession, polarized along three distinct vectors, comparable to tooth families. The teeth are composed of dentine and bone, and show a distinct pulp cavity that is infilled centripetally as development proceeds. This pattern is repeated in other placoderms, but differs from the structure and development of tooth-like structures in the postbranchial lamina and dermal skeleton of Compagopiscis and other placoderms. We interpret this evidence to indicate that Compagopiscis and other arthrodires possessed teeth, but that tooth and jaw development was not developmentally or structurally integrated in placoderms. Teeth did not evolve convergently among the extant and extinct classes of early jawed vertebrates but, rather, successional teeth evolved within the gnathostome stem-lineage soon after the origin of jaws. The chimaeric developmental origin of this model of modularity reflects the distinct evolutionary origins of teeth and of component elements of the jaws.