Milei has railed against the "thieves" of the political elite, praised gangster Al Capone for his free market credentials and on live TV smashed a piñata of the central bank, which he blames for Argentina's triple-digit inflation and intends to shut.
The 53-year-old self-proclaimed anarcho-capitalist is now pollsters' narrow favorite to win a run-off election on Sunday against Peronist economy chief Sergio Massa, his combative stance a lightning rod for voter anger at the country's worst economic crisis in decades.
"We will put an end to the parasitic, stupid, useless political caste that is sinking this country," Milei said in a speech after finishing in first place in primary elections in August, a result that shook up a political landscape long dominated by two parties.
His aggressive and theatrical style has led some to compare him to Donald Trump in the United States or Jair Bolsonaro of Brazil.
But he is a unique product of Argentina, where an entire generation has grown up under an economy in a semi-permanent state of crisis. That has sharpened this year, with inflation heading towards 150%, a sliding currency and rising poverty.
Against that backdrop, Milei and his Liberty Advances coalition have seen a dramatic rise in support, especially among the young. His campaign on social media has been helped by his colorful antics and quotes.
"He is the change that Argentina needs," said 28-year-old Milei voter Ayrton Ortiz at a rally in Buenos Aires.
CHAINSAWS, DOGS AND THATCHER
Milei's detractors point to his lack of experience in political office, his disheveled appearance - with hair that could be described as unkempt Emo - and his expletive-ridden tirades that have targeted political rivals and the pope.
"If Javier combed his hair neatly, if Javier didn't get angry, would people ever have invited him to speak?" Diana Mondino, an economist on Milei's team who would likely be his foreign minister if he wins, told Reuters.
Milei has appeared at dozens of campaign events wielding a chainsaw as a not-so-subtle symbol of the fiscal adjustments he plans to apply or else carrying a giant $100 bill bearing his face to promote his proposal to dollarize the economy.
In the U.S., comedian John Oliver dedicated a recent segment of his show to lampooning him, while former Fox News host Tucker Carlson came to Argentina for a more favorable interview.
Milei himself embraces his maverick status. He has lambasted Argentine Pope Francis as a socialist, mocked late soccer icon Diego Maradona and praised British former Prime Minister Margaret Thatcher, little loved in Argentina for her role in the 1982 Falklands War.
He has a small circle of confidants, including his 51-year-old sister Karina, who is now his campaign manager and who the unmarried Milei quipped earlier this year could become his "first lady".
His other close companion was his dog Conan, who he paid $50,000 to clone after his death in 2017. He now has at least four mastiff dogs: Murray, Milton, Robert and Lucas, named after liberal economists.
Milei claims it was Conan, contacting him through a medium, who gave him the mission to be president, and says his dogs are the "best strategists in the world."
'I AM A MISTAKE'
Many election polls show Milei slightly ahead of Massa, though pollsters have struggled to accurately predict the race so far, being caught out in both the August primary and the first-round vote last month, which Massa won by seven points.
Milei has the backing of the country's main conservative bloc, including their eliminated candidate Patricia Bullrich. That could help push him over the line on Sunday.
"I don't care who my rivals are on the ballot, I will beat them all," Milei told Reuters in an interview last year when his presidential ambitions were starting to gain momentum.
"In terms of political logic, I am a mistake, because what I have come to do is in fact stamp out the privileges of politicians."
Milei wants to end currency controls that protect the peso but warp trade, and favors laxer gun controls and tighter rules on abortion.
Juan Gonzalez, a journalist and author of a biography on Milei, "El Loco" (The Crazy One), said the presidential hopeful had stirred up excitement and even hope among voters fed up by the status quo.
But he cast doubt on the wisdom of electing a leader seeking radical change at a time when inflation is 140%, state debts are rising and a recession is looming.
"He is an unstable leader for an unstable country," he said.
(Reporting by Maximilian Heath; Additional reporting by Anna-Catherine Brigida and Eliana Raszewski; Editing by Adam Jourdan and Rosalba O'Brien)
By Maximilian Heath