And yet Trier is an unhappy place, troubled by memories of the disasters that befell the community during previous pilgrimages, and haunted by the spectre of a sinister figure from the distant past. In 1959, when the tunic could last be viewed, the war-damaged cathedral nearly collapsed under the weight of more than a million visitors. And 1933 is best forgotten. That was when Nazi stormtroopers provided the guard of honour in front of the cathedral; a poignant image of the relationship between the Church and Hitler's state.
Now was the time to heal the wounds and proclaim the unity of the Church, as symbolised by the seamless robe. But the feast has been spoilt by a row over an irreverent joke. To coincide with the event, a group of sceptics led by a lapsed Catholic decided to exhibit a garment once worn by Karl Marx, the city's most famous son. Initial outrage over Marx's underwear has since degenerated into an argument over its authenticity, throwing the dubious origins of the Holy Tunic into focus.
According to legend, disputed by some scholars, Christ's robe was brought to Trier in the 4th century by St Helena, mother of Emperor Constantine. It first makes an appearance in recorded history in 1196, and only became an object of veneration in the late Middle Ages. At some point in its history, silk and taffeta adornments were added to the original fabric, and the whole garment was dipped into a preservative rubber solution. The end result is a rigid canvas-like material with the smell of burning tyres which cannot now be submitted to scientific analysis, because the rubber treatment rendered it impervious to carbon dating.
Undaunted by the controversy, up to 30,000 people a day file past the sealed glass case containing the relic. They queue outside the cathedral for half an hour and get a few seconds to glimpse the robe and cross themselves before they must move on, to the buses which take them to the abandoned French military barracks which serve as the pilgrims' car park.
"To me it doesn't matter whether Christ wore it or not," confesses Valentin Fiedler, a 52-year-old who had driven 100 miles to behold the Holy Tunic. "What's important is that it's from His time." Mr Fiedler had "done Fatima three years ago", planned to visit Lourdes once in his lifetime, but had no intention of crossing the road from the giant pilgrims' refreshment tent to visit the art gallery that has become the Shrine of Marx's Longjohns. Not many of them do.
After the hurly-burly of the cathedral, the converted warehouse is a haven of tranquillity. There is no one to disturb the visitor's contemplation as he views the object in the eye of the storm.
It stands in a corner on the top floor, a three-winged altar made of rough-hewn wood, supporting a tabernacle encased with chicken wire that holds the fake embers. Above it, in a halo formed by wedge-shaped pieces of wood, dangle the longjohns, a slightly lighter brown than the Holy Tunic but in much better condition. Not a moth-hole in sight.
"Are they real?" I ask the altar's creator, Helmut Schwickerath, a local artist.
"Of course," he replies, struggling to keep a straight face as he launches into a long and tall story about the garment's origins. Apparently the longjohns were kept for posterity by Helena Demuth, one-time maid of the Marx household in Trier, who was made pregnant by her master and had to return to the parental home in disgrace.
The relic was handed down from one generation to the next - unworn - until it was bought by a Cuban guest-worker in the former East Germany. He took it to Cuba, where it became an object of veneration, until some tourists from Trier discovered it in the "Year of 174 After Marx" - 1992 - and brought it back to Karl's native city. It was first displayed in a local pub on Mayday 1994.
The longjohns now belong to the "Committee for the Preservation of Anti- Capitalist Artefacts", a group serious enough to be even more outraged than the local Archbishop about the artist's presentation.
"Yes, but are they real?" - I press Mr Schwickerath.
"I think it's all nonsense," he replies, no longer able to suppress his laughter. "But there are only two pairs of longjohns in the world that are claimed to have been worn by Marx, and about 20 robes attributed to Jesus. The odds are in our favour."