This article examines the international legality of the projection of Australian adjudicative and enforcement jurisdiction against non-nationals in the Southern Ocean forming part the Antarctic Treaty Area. It sets out the Australian legal foundations on which Australian jurisdiction is currently being exercised for alleged breaches of Australian law applying to the Australian Antarctic Whale Sanctuary in the HSI v. Kyodo case. It then evaluates the exercise of Australian jurisdiction in light of the applicable international law. It accepts arguendo the factual basis of Australia's territorial claim in Antarctica, but nevertheless concludes that the extension of Australian jurisdiction over non-nationals in the purported Antarctic Australian Whale Sanctuary contravenes conventional and customary international law. In light of this conclusion, the article details the nature and importance of the ATS in order to highlight what is at stake by the challenged posed by the assertion of Australian jurisdiction. It then presents reasons why (in addition to illegality) the projection of Australian prescriptive, adjudicative and enforcement jurisdiction in what almost all other states consider the high seas off Antarctica is an unsound idea. The article concludes by arguing that the current Australian law conferring jurisdiction ought to be repealed.