The tie will be played at Griffin Park on Tuesday 1st October with a 7.45pm kick-off. The Bees are currently battling for a promotion place in Nationwide Division 2 and will be a tough proposition for Steve McClaren's men.
We have played Brentford on 12 occasions before, the most recent being in the old Third Division, in the 1986-87 season just after liquidation. Boro did the double winning 1-0 away and 2-0 at home. All the previous meetings were in the old First Division either side of WWII.
The full draw is:
Stockport County v Gillingham
Crystal Palace v Cheltenham
Leyton Orient v Birmingham
Cambridge v Sunderland
Ipswich v Brighton
Sheffield United v Wycombe
Wrexham v Everton
Rotherham v Wolves
Chesterfield v West Ham
Charlton Athletic v Oxford
Tottenham v Cardiff
Aston Villa v Luton
Sheffield Wednesday v Leicester
Wigan v West Brom
Coventry v Rushden
Bolton Wanderers v Bury
Southampton v Tranmere
Brentford v Middlesbrough
Portsmouth v Wimbledon
Nottingham Forest v Walsall
Manchester City v Crewe
Huddersfield v Burnley
Derby v Oldham
Macclesfield v Preston