The two sides have enjoyed many a cup ding-dong over the years having claimed 19 titles between them.
They are bidding to join Manchester City, Arsenal and Tottenham in the semi-finals in what is already an all-star lineup for the conclusion of this year’s competition.
Here – we look at five memorable FA Cup ties between Chelsea and Manchester United…
1994 FA Cup final: Manchester United 4 Chelsea 0
Manchester United went into the final as Premier League champions, but having lost 1-0 to Chelsea home and away.
However, the Red Devils were far too strong for the Blues at Wembley as they became the fourth team of the 20th century to complete the domestic double.
It took an hour to produce the first goal, but Eric Cantona scored two identical penalties in the space of six minutes to put United in the driving seat.
Mark Hughes made it three in the 69th minute before Brian McClair rounded off victory late on.
1996 FA Cup semi-final: Manchester United 2 Chelsea 1
Manchester United came from behind to ensure they reached the FA Cup final for the third year in a row.
Ruud Gullit gave Chelsea the lead in the 35th minute at Villa Park, but United scored two second-half goals in quick succession to turn the match around.
Andy Cole netted the equaliser in the 55th minute and four minutes later David Beckham capitalised on a poor Craig Burley back-pass to score. United went on to win the final, defeating Liverpool 1-0 at Wembley.
1998 FA Cup third round: Chelsea 3 Manchester United 5
A heavyweight clash between FA Cup holders Chelsea and champions Manchester United lived up to the billing.
The visitors raced into a 5-0 lead at Stamford Bridge thanks to two goals apiece from Beckham and Cole and a Teddy Sheringham strike.
The hosts remained five goals behind with less than 15 minutes to go, but Chelsea briefly threatened an incredible comeback.
Graeme Le Saux pulled a goal back with an excellent chip over Peter Schmeichel and Gianluca Vialli scored a quick-fire double to reduce the deficit even further, but United had done enough.
2007 FA Cup final: Chelsea 1 Manchester United 0
The first FA Cup final at the new Wembley was settled in extra-time.
United had seen off Chelsea to win the league title two weeks earlier but with penalties looming after an uneventful game, Didier Drogba struck in the 116th minute to win the FA Cup for the Blues for the first time under then boss Mourinho.
2013 FA Cup quarter-final: Manchester United 2 Chelsea 2
Manchester United surrendered a two-goal lead at Old Trafford and ended up crashing out of the competition in the replay.
They raced out of the blocks as Javier Hernandez and Wayne Rooney put them 2-0 up after 11 minutes.
However, the visitors hit back in the second half and scored two goals in the space of nine minutes through Eden Hazard and Ramires.
Chelsea went on to win the replay 1-0 at Stamford Bridge thanks to a Demba Ba goal.