In their first year as a senior club, the small village side from Anglesey have taken the cup by storm and are now only game away from the quarter-finals.
In their way stand Caerphilly who only last May played French giants Castres in a European final.
But the Valleys have already proved a happy hunting ground for the Division Four outfit as they fly the flag for North Wales.
"The cup run has already exceded all our expectations but to draw a Premiership side is great for the club," said chairman Dafydd Lloyd.
"We going into territory that seemed unimaginable at the start of the season. This is our first year as a senior WRU club and I think we've already made our mark.
"Obviously we would have loved to get a home draw but this is undoubtedly the biggest cup game in our, albeit short, history and the players, coaches and supporters are going to be so excited."
Meanwhile giant-killers Brynmawr must prove they can inspire themselves against teams below them as well as above.
The First Division Gwent club knocked-out seven-time cup winners Cardiff 3-0 just after Christmas but must now travel to Corus of Division Two.
There are three all Premiership ties. Ebbw Vale will welcome three-times champions Swansea to Eugene Cross Park, 2002 winners Pontypridd head to Bedwas and Cross Keys must produce a similar performance as last if they are reach the last eight.
Cross Keys produced the surprise result of the last round with their 6-3 win over Newport but will now face Welsh cup kings, and regining champions, Llanelli.
Favourites Neath head west to play Whitland while Aberavon host Bonymaen and Blackwood travel to Bridgend.
Konica Minolta Cup 6th Round Draw
Aberavon v Bonymaen, Bedwas v Pontypridd, Bridgend v Blackwood, Caerphilly v Llangefni, Corus v Brynmawr, Cross Keys v Llanelli, Ebbw Vale v Swansea, Whitland v Neath.
All ties to be played on February 28.