Originally airing in April 1996 as part of the second series, 'A Song For Europe' remains one of the sitcom's most beloved moments.
With Eurovision 2018 taking place this weekend, we take a look back at Craggy Island's finest musical hour.
'Dougal, get the guitar'
On a restless day at Father Ted's parochial house, Dougal has got "Euro-song fever" - and is convinced he and Ted should bid to represent Ireland.
Ted insists they haven't got the talent, but upon hearing that slippery rival Father Dick Byrne is entering, ego compels him to go toe-to-toe with his nemesis.
"Dougal, get the guitar..."
It's fair to say that Ted and Dougal's bid doesn't run smoothly.
Writing an ode to a rural animal is obviously a risk at the best of times, and their song - 'My Lovely Horse' - struggles to take flight.
Over the unfolding hours, Ted devolves into a cliché of the rock n roll creative process. "Just play the f***ing note," he rants, through a haze of cigarette smoke; discarded cans and wrappers piled around them.
"[It's] not the greatest song in history; it’s just the silliest"
Much later, exhausted, all the duo have to show for their efforts is a bunch of lyrics about "fetlocks blowing in the wind", "horse dentists" - and a horribly discordant tune to go with it.
Father Jack, never one to mince his words, doesn't even bother with a "feck", "a**e" or "eejit". He simply explodes Ted's guitar into pieces with a shotgun.
"The lyrics are fine, no problem there," sighs Ted, optimistically. But what will they do about the music?
Enter Dougal's favourite song, an obscure pop number by "Nin Huguen and the Huguenotes" which finished fifth in A Song For Norway in 1976.
So obscure in fact, that Ted surmises no one will ever know if they simply lift its melody and pair it with their lyrics for My Lovely Horse. Especially as the band, their manager and everyone involved with the song died in a plane crash decades earlier.
With a cunning plan duly hatched, the priests set their eyes on stardom.
Filled with excitement, Dougal dreams of their cut-and-shut ditty being transformed into a hit pop video, complete with 'sexy' pool scene, and a psychedelic solo.
It's catchy, hummable perfection. What could possibly go wrong?
When the big day in Dublin finally comes, Ted is beset by nerves.
To make matters worse, when the hated Dick Byrne takes to the stage for his own rival turn, he flips the pair two fingers before launching into a majestic We Are The World style ballad, complete with a backing choir, showboating keyboardist, and soaring chorus.
And then everything starts to fall apart.
Upon temporarily fleeing to grab a quick, stress-abating smoke, Ted hears that the elevator music in the venue is in fact the tune they have stolen - and that people walking around the building are whistling it.
Realising that they must abandon their stolen melody and revert to their original version, lest they be revealed as the thieves they are, the inevitable happens.
When Ted and Dougal's big moment comes, the performance is catastrophic.
Clad in their glittering blue jackets, the pair flounder through an out-of-tune, mono-note rendition, like scared six-year-olds at a primary school concert (only without the benefit of a sympathetic audience).
A gleeful send-up of Eurovision
It has been suggested that Ted and Dougal's performance is a direct spoof of Ireland's 1975 Eurovision entry; right down to the suits.
But as well as poking fun at the ridiculous kitsch outfits, baffling staging and naff musical efforts of classic Eurovision, 'A Song For Europe' also makes a nod to the bizarre political machinations that often surround the contest.
Because the cost of staging Eurovision is so expensive, and the corrupt organisation committee don't want to foot yet another bill, Ted and Dougal are adjudged the winners and become Ireland's entry - as there's no way they will possibly triumph in the competition proper.
In real life, Ireland had indeed won three times on the trot between 1992 and 1994.
"When we did the Song for Europe episode, British people were aware that Ireland was always winning Eurovision and that there was a rumour we didn't want it, because we kept having to stage it," explained Father Ted co-creator Graham Linehan.
So the hapless priests end up being packed off to the Eurovision finals. Where, of course, they end up going home with a resounding "nil points" - forced to suffer the indignity of sitting shame-faced in the Eurovision green room as the results are read out, and the episode's credits roll.
Ireland has a long and illustrious association with Eurovision. They are the most successful nation - with seven wins to date - while the late, great Terry Wogan made withering coverage of the competition a speciality. A tradition that compatriot and Father Ted supporting actor Graham Norton now gleefully continues.
'I knocked it out in half an hour'
My Lovely Horse (the good version) was written by The Divine Comedy's Neil Hannon, who also composed the title theme for Father Ted.
Over the years, he has found himself bemused and delighted by its enduring appeal.
"My Lovely Horse will probably be on my gravestone because it’s the song which is shouted for at my live shows more than any other," joked the singer, in a 2011 interview.
"It’s insane. I knocked it out in half an hour. [It's] not the greatest song in history. It’s just the silliest."
Hannon has since reprised the track live.
Sadly, the chances of a My Lovely Horse esque ditty from Hannon appearing on Eurovision proper are slim.
Last year the singer said he was unlikely to write an entry for the contest, saying it had lost its "fun cheesiness" in favour of a "serious" streak.
And politicians have also put a stop to Hannon's original creation making the cut.
In a wonderful case of life imitating art, in 2014 a fan petition attempted to see My Lovely Horse become Ireland's official entry in the contest. But a parliamentary committee ruled against putting it to a vote.
Members "didn't have the musical expertise" needed to consider the issue, they claimed.
Father Ted is available to watch on All4 now
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This article originally appeared on our sister site, iNews.
[Main image: Channel 4]