The Swans are chasing a first appearance at a major Wembley final. Given Bradford and Aston Villa are the other sides left in the competition, Swansea fans could be forgiven for cursing their luck when they drew Rafael Benitez's Blues in the last four.
The Swans have never previously got to this stage of the League Cup, although they did reach the last four of the FA Cup in 1964, although there will be few expecting them to triumph over two legs against a Chelsea squad including Demba Ba, Juan Mata, Eden Hazard and Frank Lampard.
But Swansea have a good home record against the Premier League big guns and have twice drawn 1-1 with the Blues at the Liberty Stadium, but their only visit to Stamford Bridge since returning to the top-flight ended in a 4-1 defeat.
Laudrup knows a repeat scoreline on Wednesday night would effectively end the tie, but is excited at the prospect of being able to bring the Blues back to south Wales with the tie still in the balance.
He said: "I always preferred being away first in these games. I have done both as a manager and a player and if I had to choose I would prefer to play away first.
"The different thing is it is not a complete game, it is only the first half and we play the second half here in two weeks' time.
"It is difficult to play a game when you know you have another one to come, but we know it is important to get a result so we can play the second leg here in front of our fans with the possibility to go through.
"It will be difficult, we know that. To beat Chelsea in one game is difficult, over two games it is even more difficult.
"But we have to give it a try, and we will give it a try and I hope the confidence we have built up in recent weeks can help us."
Following Sunday's FA Cup draw with Arsenal, Swansea's resources are set to be stretched over the course of a month which could see them playing nine games in total.
Premier League survival remains Swansea's priority, but with a place in the final up for grabs, Laudrup will not be holding any of his players back.
"As a smaller club we cannot normally compete for trophies, so to be so close to a final is fantastic," he said.
"It is the first time for us to be in a semi-final for some time.
"It is the first time since 1964, that was a good year as I was born then so it is 48 years ago and it shows what an achievement this is.
"The chance to go and play in a final is very big for us."
Laudrup also refused to discuss any transfer window activity ahead of the trip to Stamford Bridge.
Speculation continues to link striker Danny Graham with a move away from the club, with Aston Villa and Sunderland reportedly his latest suitors.
But reports linking him with an imminent switch appear wide of the mark as he trained on Tuesday and will be part of the squad at Stamford Bridge.
But Laudrup said: "I know it is January and you are always going to ask me about transfers this month, but the game is so important for us so today there is no comment on anything other than Chelsea.
"There will be nothing on Danny Graham or anyone else as the most important thing is the game tomorrow [Wednesday]. It is huge for the club, the players and all of us and that is the message we have to send."