With only eight Premiership sides left in the last 16, bookmakers William Hill are giving odds of 16/1 for Blues to lift a trophy they have never won.
Arsenal are 5/2 favourites to win the Cup with Hills who make Manchester United 3/1 second favourites, Chelsea third favourites at 100/30 with Liverpool next at 7/1.
Other prices:
Spurs: 16/1
Fulham, Man City & West Ham: 25/1
Everton: 28/1
Portsmouth: 33
Sheff Utd: 40/1
Sunderland: 50/1
Burnley, Millwall: 66/1
Coventry, Tranmere: 150/1
Swansea: 300
Colchester: 400/1
Telford: 1000/1