It is 13 seasons since Arsenal last lifted a European trophy - the 1994 European Cup Winners Cup.
Wenger has reached three European finals - and lost them all
Alan Smith struck early and Arsenal then repelled attack after attack from a Parma team that contained the likes of Gianfranco Zola, Faustino Asprilla and Thomas Brolin.
Lee Dixon was a member of Arsenal's defence that May evening in Copenhagen and has fond memories of that 1-0 win.
"There is something special about winning in Europe," he told BBC Sport.
"From a defensive point of view it was a great achievement because we got battered by Parma."
Another European campaign for the Gunners starts on Wednesday when they take on Sparta Prague for a place in the group stage of the Champions League.
It will be Arsenal's 10th successive European campaign under Arsene Wenger.
Since the 57-year-old was officially named Arsenal manager on 28 September 1996, the Gunners have won the FA Cup and Community Shield four times and the Premier League three times.
It is a mystery why Arsenal have not done better in Europe
Wenger has been manager of the year three times, received an honorary OBE from the Queen and been made a Legion d'Honneur.
But for all his achievements, a European trophy remains conspicuously absent from Wenger's managerial CV.
"I think it is a big frustration for him," French journalist Xavier Rivoire, author of a recently published biography of the Arsenal manager, told BBC Sport.
"This is perhaps made worse by the fact that his teams have reached finals without actually winning them."
Wenger has reached three European finals as a manager, the first of which was Monaco's 2-0 defeat by Werder Bremen in the 1992 European Cup Winners' Cup final.
Arsenal lost the 2000 Uefa Cup final on penalties to Galatasaray and six years later Wenger's team were defeated 2-1 by Barcelona in the Champions League final in Paris.
And Dixon, who was in the team in 2000, agrees that Wenger's failure to win in Europe is a source of great frustration.
"I think everybody is surprised that Arsenal have not won a European trophy since 1994 - and certainly the man that counts, Arsene Wenger," said Dixon.
"He has been bitterly disappointed with how Arsenal have failed to go on, reaching the quarter-finals several times and then getting knocked out.
"It is a mystery why they have not really gone on."
Dixon was in Paris to watch the 2006 final and felt that Arsenal had a great chance to win the match.
"I thought they should have won against Barca," said Dixon. "It was a big stride in getting to the final.
"There was a time when Arsenal had the game under control but then the complexion changed completely.
"Arsenal had a young side and when things go wrong inexperienced players start looking over their shoulders. I'm not sure they had enough leaders."
ARSENAL'S EURO RECORD UNDER WENGER
1997-98: Uefa Cup, 1st round, lose to PAOK Salonika
1998-99: CL, 1st group stage
1999-2000: CL, 1st group stage
Into Uefa Cup, lose final
2000-01:CL, QF, lose to Valencia
2001-02: CL, 2nd group stage
2002-03: CL, 2nd group stage
2003-04: CL, QF, lose to Chelsea
2004-05: CL, last 16, lose to Bayern Munich
2005-06: Final, lose to Barcelona
2006-07: CL, last 16, lose to PSV
*CL denotes Champions League
Dixon feels that Arsenal have been a touch naive at times in recent years and a little vulnerable defensively, especially away from home.
But he is optimistic for the current season, arguing that a lot of the players are mature beyond their years while the return to fitness of Robin van Persie will make a big difference to the side.
And he is in no doubt of the importance of beating Sparta in the first leg.
"A good start is especially important with a young side because they could drop their heads. Getting through to the next stage will breed confidence."
And although Wenger is less than thrilled with such important European games arriving so soon in the season Dixon acknowledges that it is the price to be paid for last season.
"Finishing fourth in the Premier League is not good enough for a club of Arsenal's size - and when you finish fourth you have to take your medicine," stated Dixon.
But for those who feel that Arsenal's chances of European success this season disappeared with the departure of Thierry Henry to Barcelona, it is worth bearing in mind what happened the last time a talismanic figure was sold.
"When they reached the Champions League final in 2006 nobody thought they would make it at the start of the season," said Rivoire.
"They had lost Patrick Vieira the previous summer and people said Arsenal would never be the same."