Roberto Di Matteo's side claimed a 5-4 extra-time victory over the Red Devils after forcing the additional period courtesy of Eden Hazard's last-gasp penalty.
The Blues' trip to Elland Road will excite both sets of fans, while Ken Bates - former owner of Chelsea and currently in the process of selling Leeds - will be another interested observer.
Neil Warnock's side have already dispensed with two top-flight opponents in the competition, knocking out Everton 2-1 and Southampton 3-0 - both on home turf.
Chelsea boss Di Matteo told Sky Sports: "Playing away is always difficult and Leeds and Chelsea have a bit of history there as well.
"It will be an interesting game."
The lowest-ranked side still in the hat, npower League Two outfit Bradford have been dealt a tough draw against Arsenal but at least have the benefit of home advantage.
Like Leeds the Bantams have already knocked out Premier League opponents, seeing off Wigan 4-2 on penalties after yesterday's 0-0 draw.
For an Arsenal side looking to end a trophy drought stretching back to 2005, the chance of a taking on a fourth-tier side for a place in the semi-finals must surely be an appealing one.
Aston Villa's trip to Norwich is the only all Premier League match-up in the last eight and gives Villa boss Paul Lambert another chance to face the club he left this summer.
The two teams drew 1-1 in league action at the weekend.
The draw is completed by Swansea's home match against Middlesbrough.
Boro earned their place in the quarter-finals with a derby victory over Sunderland in the fourth round, while Swansea tonight defeated their former manager Brendan Rodgers' Liverpool side at Anfield.
Fixtures are due to take place on the week commencing December 10, barring Leeds versus Chelsea which is deferred until December 19 due to the latter's participation in the World Club Cup.
Capital One Cup Quarter-Final Fixtures
Leeds vs Chelsea
Swansea vs Middlesbrough
Norwich vs Aston Villa
Bradford vs Arsenal