The Scarlets have failed to win on three previous occasions in Glasgow and, quite simply, their record on Scottish soil is pretty poor. As well as three defeats in the Welsh/Scottish League in Glasgow, they lost on their three visits to Edinburgh in the same tournament and were outgunned by the Scottish Borders in their first away game in the Heineken Cup back in 1996.
In fact, the only competitive triumph the Scarlets can point to in Scotland is against Caledonia in the 1997/98 Heineken Cup competition when they squeezed past the home side 23-18.
"We have got to go and win a game and not think about what has gone on in the past," said coach Gareth Jenkins.
"We have yet to beat Glasgow north of the border but this time we won't be playing for two points, but a place in the quarter-finals of the Heineken Cup."
A key player for Llanelli is sure to be former Wales captain Scott Quinnell, who produced one of his "specials" against Bourgoin in their 37-22 victory in Round 5.
"We have got a huge week, it is one of the most important in the club's history," said the powerhouse No 8.
"We have got to go to Glasgow and make people proud. It is a must-win game for us. The victory over Bourgoin was one of those great Heineken Cup nights at Stradey Park and we will be doing our best to get the win we need in Scotland to carry our club and supporters through to the last eight."