Ole Gunnar Solskjaer's men booked their place in the last-16 after beating Arsenal 3-1 at the weekend.
But now they will have to battle past the Blues if they are to continue their quest of silverware under the Norwegian caretaker boss.
That means, should Manchester City – who take on Middlesbrough or Newport – win, only TWO of the Premier League's top six will be in the pot for the quarter-finals.
In fact, in the round-of-16 draw, there are only seven top-flight teams left.
The winner of Brighton and West Brom will take on Derby, while Wolves or Shrewsbury will travel to Bristol City.
FA Cup fifth-round draw
Bristol City vs Shrewsbury OR Wolves
AFC Wimbledon vs Millwall
Doncaster vs Crystal Palace
Middlesbrough OR Newport vs Man City
Chelsea vs Man United
Swansea vs Barnet OR Brentford
Portsmouth OR QPR vs Watford
Brighton OR West Brom vs Derby
Crystal Palace travel to Doncaster, while the victor of QPR vs West Brom will host Watford.
Meanwhile, there's as tantalising clash lined-up for the last-16, as AFC Wimbledon play host to Millwall.
The Dons beat West Ham 4-2 this weekend to set up the clash, while the Lions beat Everton.
All eight fifth-round ties will be played between February 15 and 18.
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