I investigate the extent to which there might be, now or in the future, non-human animals that partake in the kind of fully human-style consciousness (FHSC) that has been taken by many philosophers to be the basis of normative personhood. I first sketch a conceptual framework for considering the question, based on a range of philosophical literature on relationships between consciousness, language and personhood. I then review the standard basis for largely a priori skepticism about the possibility that any non-human animal could experience FHSC and be a person to any extent, and indicate empirically motivated grounds for rejecting such skepticism, at least with respect to a select group of hypersocial candidate species with communication systems we do not currently know are not languages: corvids, parrots, elephants, and toothed whales. Relevant facts about elephants are reviewed in some detail, as a mini case study. While it is suggested that elephants might partake in the sort of consciousness characteristic of personhood to some extent, grounds are given for expecting that this extent is sharply limited by comparison with normal humans. As these grounds are mainly aspects of elephants’ external niche, however, rather than known limitations in their inboard cognitive or representational capacities, the surprising conclusion emerges that elephants might acquire FHSC, and thereby become persons, if they can be brought into conversation with humans, a possibility opened by considerations canvassed in the paper.