By virtue of the Antarctic Treaty, signed in 1959, the territorial claims to Antarctica of seven of the original signatories were held in abeyance or “frozen.” Considered by many as an exemplar of international law, the Antarctic Treaty System has come to be increasingly questioned, however, in a very much changed global scenario that presents new challenges to the governance of the White Continent. In this context, it is necessary to gain a clearer understanding of the moral weight of those initial claims, which stand (despite being frozen) as a cornerstone of the treaty. The aim of this article is to offer an appraisal of such claims, which may be divided into two main kinds: those grounded on some relevant link to the territory, and those grounded on official documents and geographical doctrines. After pointing to the limitations and challenges that they face, I conclude with some remarks about how this assessment ought to serve as a starting point to rethink the territorial status of Antarctica.