The Hammers were desperately unlucky to be held to a 1-1 draw by Manchester United in the FA Cup on Sunday after more magic from their hero Dimitri Payet.
His sumptuous late free-kick looked to have given Slaven Bilic's men a deserved place in the semi-finals at Wembley.
But Anthony Martial bundled home a scrappy equaliser to set up a fitting last ever FA Cup game at West Ham's Boleyn Ground home of 112 years ahead of their big move to the Olympic Stadium this summer.
The East Londoners go into the game bang in form as they are unbeaten in seven and have won five of those, drawing the other two.
Chelsea on the other hand are out of all competitions and are sitting midtable after a disastrous season.
They will also be missing key striker Diego Costa after his sending off in the defeat to Everton last time out.
Stamford Bridge has not been a happy hunting ground for West Ham in recent years.
But everyone at the club has been buoyed by their fantastic season so far, which has included the double over Liverpool, wins at Manchester City and Arsenal and victories over Tottenham Hotspur and Saturday's opponents Chelsea in the reverse fixture.
'It is still a very, very hard game'
And co-owner Sullivan is no different, telling the club's official website he is brimming with confidence.
"Despite their (Chelsea's) recent results in the cup competitions, it is still a very, very hard game," Sullivan told whufc.com.
"We are 9/2 to win and the bookies only give us a 38% chance of getting anything out of the game, but I don't feel we will come away empty handed.
"We have a good record against the London clubs this season and I hope that will continue at Stamford Bridge on Saturday."
So there you have it Sullivan is obviously hoping for a win but believes the Hammers will get at least a draw in West London.
Victory would put the Hammers 12 points ahead of Chelsea in the Premier League table while a win for Guus Hiddink's men would close the gap to just six points.