I heard recently that Argentina was on the short list of nations America was worried would get the bomb. I've never heard of Argentina being considered like that, or even remotely considered a nuclear power. What was their project like and why was America so worried?
Argentina was the most advanced South American nation in nuclear technology, and during its period of dictatorship in particular there were worries that it and Brazil would engage in a regional nuclear rivalry. They created the Comisión Nacional de Energía Atómica (CNEA) in 1950 under Juan Perón to coordinate and fund their nuclear research, at a time when many nations of that size/stature were doing similar things. They were one of the many countries that the US signed a bilateral agreement with on cooperation for civilian research on atomic technology (a research agreement active from 1955-1962; the US had a similar agreement with Brazil for nearly exactly the same dates, as an aside).
In the 1960s, they spurned the Nuclear Non-Proliferation Treaty (their ambassador to the UN decried it as "disarmament of the disarmed") and in the 1960s and 1970s built up an un-safeguarded nuclear fuel cycle (including uranium enrichment and plutonium reprocessing) that could have been used towards the development of the fuel for nuclear weapons. They were the first South American nation to have an operating nuclear power plant (in 1974). But they never made the political decision to make nuclear weapons, and after the military rule ended in 1983 it seems like that avenue was largely avoided, in part aided by improvement of relations with Brazil, and in the 1990s both nations signed the NPT.
The only other interesting side story is that Perón sponsored a very unusual project — the Huemul Project — in which an ex-Nazi scientist, Ronald Richter, was given free reign of an island to try and create nuclear fusion. It was not at all a success, but premature announcements of supposed accomplishments were what began the US peaceful nuclear fusion program.
I don't have more details than that, but it is worth emphasize that as far as we know they never had a nuclear weapons program. They did have a very ambitious nuclear power program, and set it up in a "dual use" way that could, if they had chosen to, converted it into a program for making the fuel for a nuclear weapon — perhaps the most difficult part of becoming nuclear-armed (they would still have to design the weapon itself, probably test it, and also design and test the delivery systems).
The Nuclear Threat Initiative has a concise discussion of some of the history and the facilities that are currently part of their nuclear program.