Well, for starters, Argentina would also have them, both countries started their nuclear programs around the same time and agreed to dismantle them together (with mutual control on each other), with the creation of ABACC. (
https://en.wikipedia.org/wiki/Brazilian–Argentine_Agency_for_Accounting_and_Control_of_Nuclear_Materials)
I'm not sure the US would allow either country to develop nuclear weapons, however. The marines would be knocking at the door as soon as the first nuclear test was close to taking place.
In real life, democratization happened in the 1980s, and the hand of the US was not forced, backdoor diplomatic pressure was enough to guarantee non-proliferation.
In a timeline in which any of the two countries was serious about it, I imagine the US would intervene, either through sanctions, covert CIA warfare, or actual military intervention.
And every single other state in South America not capable of developing their own nuclear weapons would be thanking the Americans for their intervention, from Venezuela to Chile.
Even as democracy consolidated and Argentina was named a Major Non-NATO Ally of the US in 1998, there was still American pressure to make sure all research in the Condor Missile (Medium Range Ballistic Missile) was ended and every single specimen destroyed.
If the US went through all the trouble it did to stop a ballistic missile, nukes would definitively be out of the question for any South American state. Some toys are just not allowed.