Eh, no? It was indian/no one's territory. Both Chile and Argentina had (more or less equally valid) claims to it. The difference was that Chile couldn't realistically project power to the other side of the Andes so when Argentina said "I keep everything east of the Andes, you get the rest" they weren't able to object much.
I mean really, that land was as chilean as it was argentine. That is to say, it wasn't.
As was the Beagle Channel? the Southern Patagonia Ice Field? The Puna de Atacama Dispute? The Cordillera of the Andes Boundary Case? all those are Argentina Trying to Claim Chilean Territories with Treaties where they Accept they are Chilean Territories. I insist most of the Diplomatic Tension between Santiago and Argentina is Buenos Aires bid, not Santiago Hell Chile Even give up Half of the Isla Grande de Tierra del Fuego, with the intention to maintain good diplomatic relations, when Chile have control of all the Island and the only settlement in the Region, Punta Arenas founded in 1843, in the, vain, objetice to maintain peace and friendships between the countries.