It is the startling, occasionally surreal story of a Kerry-born circus strongman, a convicted killer and the 20th century sports icon known simply as The Greatest.
The film centres on the fight, in Croke Park, between Ali and the American challenger Al "Blue" Lewis, an ex-convict who miraculously won parole from a life-sentence for murder in his native Detroit.
They were brought together in Dublin by an ex-circus strongman from Kerry, a colourful bar-owner who billed himself as "The World's Strongest Publican".
Ali, the descendant of slaves, was returning to the land of his paternal great grandfather, Abe Grady, an immigrant from Ennis, Co Clare. And as a convert to the Nation of Islam, Ali had mixed feelings, to say the least, about his white Irish heritage.
However, When Ali Came to Ireland reveals how the reception he got here, at the time "the whitest country on the planet" as one contributor puts in, helped to change the boxer's views of white people.
Made by the award-winning film-makers Ross Whitaker and Aideen O'Sullivan, the hour-long doc by their Dublin based True Films, gets its broadcast début on RTÉ One on New Year's Day.
And if a recent, sold-out preview screening at the Irish Film Institute in Dublin is anything to go by, When Ali Came To Ireland should be one of the big highlights of a very packed Christmas schedule on TV.
The story focuses on the events of July 1972, when former champ Ali, recently released from prison after being jailed for refusing to fight in the Vietnam War, is on the comeback trail.
There were opportunities for foreign fight promoters looking to cash in on the Ali aura. And that's where the highly unlikely figure of Michael "Butty" Sugrue from Killorglin, Co Kerry, popped into the picture.
Sugrue, an ex-circus strongman with a flair for bizarre publicity stunts (and some of his antics provide genuine laugh-out-loud moments in the documentary) saw his chance.
Butty was able to persuade a well-known American promoter, with ties to the Ali camp, that he could bankroll a fight in Croke Park in Dublin on July 11, 1972.
Ali arrived at the start of July and stayed in a newly built hotel just outside Dublin. His entourage included movie star Yul Brynner's son Rock and various US journalists and fight figures who set out to have a high old time in Dublin.
The lead up to the fight was a catalogue of setbacks for the promoters. Even with tickets for the showdown on the pitch at Croke Park costing as little as six pounds, there were not a lot of takers.
In the end, some 20,000 people bought tickets. Thousands more simply jumped over the wall at Croke Park or were let in by security staff who were not exactly doing a rigorous job.
Ali stopped his opponent in 11 fairly lack-lustre rounds. Butty Sugrue, the Kerry publican turned fight promoter lost his shirt and the Ali Bandwagon rolled on to bigger nights in more exotic climes in the Far East.
Director Ross Whitaker, who has spent several years making the documentary, says he was inspired to get into making films by the classic Muhammad Ali documentary When We Were Kings.
"After I saw that back in 1996, I started looking into film courses and also reading everything I could about Ali," says the Dubliner.
"And I found out that Ali had fought in Ireland but that it was only ever given a few lines in any biographies, so that's when I began to hatch the idea of doing a film on Ali in Dublin."
Ross has uncovered some great archive footage from the summer of 1972 – including a classic interview between RTÉ's Cathal O'Shannon and Ali, which was secured by the national broadcaster for the princely fee of £100. Michael Parkinson had just paid Ali £14,000 to appear on his chat show in England.
Ross conducted the last ever interview with O'Shannon, who talked about his encounter with Ali, shortly before his death.
"It was an amazing piece of good fortune that we were lucky enough to talk to Cathal before he died," says Ross. "He says himself that the Ali interview put him on the map and he was happy to be remembered for it."
The footage of Ali at RTÉ and the amazing photos of him playing hurling with Kilkenny great Eddie Keher – who got to meet The Greatest as one sporting hero to another – are just two elements of a brilliant film that captures a fascinating, now almost forgotten moment.
When Ali Came To Ireland – RTÉ One – 6.30pm New Year's Day.