He thinks Bill Gates is trying to control the world through 5G, has compared Covid jab mandates to the treatment of Jews during the Holocaust and says he often has "conversations with dead people".
Yet many are beginning to believe Robert F. Kennedy Jr will beat US President Joe Biden for the 2024 Democratic nomination - and have a good chance of entering the White House next year.
The 69-year-old has long been considered a dangerous eccentric, disowned even by his family, and the least likely person to revive the Kennedys' political fortunes.
He believes it was the CIA, not Lee Harvey Oswald, who killed his uncle, former President John F. Kennedy in 1963, and has made similar claims about the assassination of his father, presidential candidate Robert F. Kennedy, in 1969.
Such bizarre outbursts led him to be dubbed the "Democrats' Trump" when he announced his candidacy last month, to sniggers from politicians and the press.
But since then, just like Mr Trump, he has confounded doubters with an unexpected surge in support.
One poll last week put him at 20% among Democratic primary voters - unheard of for an outsider with nearly a year before they decide.
Another found 44% of Americans view him favourably, compared with 40% for Mr Biden, while only 22% saw him unfavourably, compared with 58% for the President.
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