The Blues, who hammered fellow top-flight side Southampton 5-1 to reach this stage, will visit either League Two Southend or Brentford of League One in the next phase after their 2-2 draw at Roots Hall on Satuday.
Premier League champions Manchester City were also handed a potentially tough away-day assignment against the winners of the replay between Championship side Crystal Palace and Stoke, who lost 1-0 to City in the 2011 final.
Non-league Luton's reward for their victory over Wolves is a trip to Carrow Road to face Premier League Norwich, with Newcastle's conquerors Brighton welcoming the winners of the replay between Swansea and Arsenal to the Amex Stadium.
Oldham, who impressed in defeating Nottingham Forest, will face Liverpool, while on-league Macclesfield, surprise winners against Championship pacesetters Cardiff, will welcome Wigan or Bournemouth.
There were no guaranteed all-Premier League matches in the draw, although one or two are in the pipeline after West Ham or Manchester United were pitted against either Fulham or Blackpool, while Sunderland and Everton could meet if they can overcome Bolton and Cheltenham respectively.
Tottenham face a potentially tricky away trip to Championship opposition, with the winners of the replay between Leeds and Birmingham lying in wait. Paul Lambert's Aston Villa are also on the road to play Millwall.
Reading entertain Sheffield United, while QPR or West Brom, who drew 1-1 at Loftus Road on Saturday, will battle for the right to host Sheffield Wednesday or MK Dons in their replay.
Two all-Championship ties see Huddersfield host Leicester and Derby welcome Blackburn, while Aldershot are away to Middlesbrough and Barnsley lie in wait for the winners of the replay between Hull and Leyton Orient.
The draw for the fourth round of the 2012-13 FA Cup:
Norwich v Luton
Oldham v Liverpool
Macclesfield v Wigan or Bournemouth
Derby v Blackburn
Hull or Leyton Orient v Barnsley
Middlesbrough v Aldershot
Millwall v Aston Villa
Leeds or Birmingham v Tottenham
Brighton v Swansea or Arsenal
Crystal Palace or Stoke v Manchester City
West Ham or Manchester United v Fulham or Blackpool
Southend or Brentford v Chelsea
Reading v Sheffield United
Huddersfield v Leicester
QPR or West Brom v Sheffield Wednesday or MK Dons
Bolton or Sunderland v Cheltenham or Everton
Ties will take place on the 26/27 January