Vidal, by contrast, was so pleased with his own performance that, into old age, he would often invite guests to watch videos of the debates after dinner. “Gore was obviously a narcissist,” says Parini, “and what a narcissist most craves is maximum attention. He never had that level of national attention again – after that it was sort of a gentle slide to the grave.”

The pair managed to keep their feud going with a lawsuit that lasted several years, Buckley suing Vidal for implying he was secretly gay, and Vidal counter-suing. Buckley died in 2008, Vidal four years later.

Who was the real winner? “As we discuss in the play, the short-term win went to Gore but I think the long-term victory was Buckley’s,” says Graham. “It’s hard to imagine now, but conservatism didn’t really have a foothold in American politics in the 1960s. But Buckley’s ideology [free-market capitalism and libertarianism] became that of the establishment parties in the US and here; he basically wrote Ronald Reagan, created him as a character.”

This play – a co-production between the Young Vic and the touring theatre company Headlong – presents Graham with a similar challenge to the one he faced with Quiz, his play about the Who Wants To Be a Millionaire? cheating scandal: taking events on TV and making them three-dimensional.

His solution, he says, has been to imagine, in partnership with Bunny Christie, the set designer, “a fluid space which transforms from the TV studios into many other kinds of public squares: the Cambridge Union [where Buckley famously clashed with James Baldwin over civil rights in 1965], the streets of Chicago.

“What we want to create… is a real sense of congregation and public gathering. Also, I hope it’s funny. You can’t write a play with Gore Vidal and William Buckley and not make people laugh, I hope.”

Best of Enemies is at the Young Vic, London, December 3 – January 22. Tickets: 020 7922 2922, youngvic.org