Chile-Argentina rivalry is almost as old as the countries - they were initially allies in the 1830s vs Peru-Bolivia but went into border dispute with southwards expansion into Patagonia, and only really normalised in 1984 (Tratado de Paz y Amistad de 1984 entre Chile y Argentina). At one point US army even wanted to invade Chile using Argentina as base of operations (Baltimore crisis). Of course everything can easily sour again over shipping through Strait of Magellan, or, if Antarctica claims get unfrozen on international level, for resources in Antarctica.
Bolivia is a wildcard if China meddling and lithium mining becomes a factor.