The game at Llandovery's Church Bank ground will be one of only three all-Premiership clashes. The others see Cross Keys host Bedwas and Carmarthen Quins entertain Pontypool.
The reward for their battling performances to date in the tournament for the last surviving Welsh Districts club, Bryncethin Sports, is a home tie against ASDA League Division One side Caerphilly.
Bryncethin accounted for Bala in round one, 28-8, and Seven Sisters, 21-17, away from home in round two. Now they have an even bigger scalp in mind in December.
Newly promoted Premiership side Glamorgan Wanderers will host Division One's Ystrad Rhondda in one of the closest games to call, while Aberavon will also have home advantage over a Division One team, Fleur de Lys.
Last season's beaten finalists, Pontypridd, will travel to Division Two West side Pontyberem, while Swansea won't be relishing their trip to high flying Corus of the same division.
The 2004 champions, Neath, will ensure a bumper crowd at Taffs Well, the unbeaten leaders of Division Four South-East, and Ebbw Vale will also have to travel to Division Four South-West club Heol y Cyw.
The sole surviving north Wales club, Nant Conwy, will be fancying their chances of making it three home wins in a row after being drawn against Division Three South-East's Tylorstown. They have already seen off Maesteg Quins, 32-0, and Hirwaun, 48-8, on their own patch and will be seeking to ride into round four with another convincing win.
Cardiff face a tricky trip west to Laugharne, while Premiership Maesteg's home clash with Kenfig Hill will give the Division Three South-West side the chance to cause an upset.
Bridgend host Division One side Cwmllynfell and Newport host Beddau.
KONICA MINOLTA CUP THIRD ROUND DRAW (matches to be played on the weekend of 3 December)
Aberavon v Fleur de Lys
Abercynon v Machen
Blackwood v Rhydyfelin
Bridgend v Cwmllynfell
Bryncethin Sports v Caerphilly
Brynithel v Pencoed
Cardiff HSOB v Kidwelly
Carmarthen Quins v Pontypool
Corus v Swansea
Cross Keys v Bedwas
Glamorgan Wanderers v Ystrad Rhondda
Heol y Cyw v Ebbw Vale
Laugharne v Cardiff
Llandovery v Llanelli
Maesteg v Kenfig Hill
Merthyr v Cilfynydd
Mumbles v Llangennech
Nant Conwy v Tylorstown
Narberth v Barry
Newport v Beddau
New Tredegar v Newport Saracens
Penallta v Bonymaen
Penclawdd v Glycorrwg
Pontyberem v Pontypridd
Pontypool United v Llanharan
Taffs Well v Neath
Taibach v Dunvant
Tonmawr v Mountain Ash
Tonna v Pill Harriers
Trebanos v Builth Wells
UWIC v Llantwit Fardre
Whitland v Bridgend Athletic
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