And they can also become the first side to claim three European trophies in consecutive seasons.
Both London Wasps and Leicester Tigers have previously done the double - Wasps with back-to-back Challenge and Heineken Cup titles in 2003 and 2004 and the Tigers with consecutive Heineken Cup crowns in 2001 and 2002.
But while 2009, 2011 and 2012 Heineken Cup champions Leinster can move a giant step closer to a unique piece of history in the Champions Challenge clash, Biarritz will be determined to defend their own crown.
The Basque giants edged past Toulon at the Twickenham Stoop to lift the Amlin Challenge Cup last year, with dead-eyed talisman Dimitri Yachvilli landing seven penalties.
They have a wealth of talent across the pitch with the likes of Imanol Harinordoquy, Damien Traille, Iain Balshaw and Taku Ngwenya within their ranks.
And, while they have proved they have pedigree on the road with victories over Wasps on the way to the 2012 final and against Gloucester in this season's quarter-finals, they will have the massive additional motivation by the carrot of automatic qualification for the 2013/14 Heineken Cup tournament.
They currently languish 11th in the Top 14 and warmed up for their European day of destiny with a 14-0 defeat to Bordeaux Begles.
Meanwhile Leinster are fighting on two-fronts with a place in the RaboDirect PRO12 play-offs already secured.
The Dubliners have won 12 of their 14 matches since being put to the sword by Clermont Auvergne, including an away victory over Heineken Cup semi-finalists Munster two weeks ago.
They will also have the motivation of setting up a fitting finale for several key players.
Isa Nacewa and Jonny Sexton, both integral in their previous Heineken Cup triumphs, will bid farewell to the club in the summer and if successful against Biarritz, Leinster will also have the advantage of the Amlin Challenge Cup final being held at their home ground at the RDS on Friday, May 17.
• Leinster have faced Biarritz on five occasions in the Heineken Cup. They have won three and lost two of those, though their last meeting came in January 2004.
• Jamie Heaslip has made more carries than any other player in ERC competitions this season; the Ireland captain has carried the ball on 95 occasions so far.
• Leinster have lost their last two matches against French opposition in Europe (both v ASM Clermont Auvergne this season) but were unbeaten in their previous six.
• Takudzwa Ngwenya was the top metre-maker in the Amlin Challenge Cup quarter-finals, carrying the ball for 163 metres.
• Biarritz have reached five ERC semi-finals before and have advanced from the last four in three of those matches.