Could there have been natives of Antartica, probably on the northern tip of that peninsula? Or is this ASB?
I'm sure that there are others on the board who have better knowledge of matters such as these than I do, but here are my thoughts.
I first thought of the indigenous peoples of the Arctic. Their diet is primarily whales, walrus, caribou and seal. The Antarctic (particularly the Antarctic Peninsula) would provide a source of these: the Antarctic fur seal, leopard seal, Weddell seal, southern elephant seal, crabeater seal, blue whales and orcas are all found in and around Antarctica, as well as fish in the seas. Presumably penguin eggs, if not their meat, could also provide another food source (Polar explorers did eat penguin - it was presumably not delicious, but in a scarce environment, it is food. Some of the natives of Tierra del Fuego ate penguins from time to time). Inuit also eat algae, which is found around the Antarctic Peninsula, as well as grasses, tubers, roots, stems and berries. The Antarctic has very few vascular plants, though the majority of these are found in the Peninsula. Presumably there are ways to eat mosses and Antarctic hair grass and Antarctic pearlwort...but it's not going to do much for you. Luckily plant matter is almost insignificant to the Inuit diet. So as far as food is concerned, I think a small population could survive.
Next, where would people come from? Presumably they would spread south from Tierra del Fuego. I don't know if this would have been possible. While the indigenous peoples of Tierra del Fuego had boats, they were small craft incapable of covering the 1000+ miles from Tierra del Fuego to the Antarctic Peninsula. I don't think that Antarctica was connected to South America during the last ice age, so humans couldn't have walked across. Perhaps Polynesians could have reached Antarctica - but why would they have stayed? The furthest south they went was the Auckland Islands, and they didn't bother staying there long - and the Auckland Islands are positively inviting, compared to Antarctica.