Michael Laudrup's side travel to Stamford Bridge on Wednesday night before the return leg in Wales on 23rd January, and Vorm has taken encouragement from Queens Park Rangers' shock victory over the Blues in the Premier League.
"What QPR achieved last week can inspire us. After Chelsea beat Aston Villa 8-0, everyone wrote off QPR. But they went there and won," Vorm said in the Daily Express.
"Everyone is so competitive; that is why I love English football. And Chelsea will not know what to expect from us.
"We have to believe in ourselves and give everything until the very end."
Vorm appreciates what a difficult task it will be against Chelsea but says Swansea will go into the tie believing they can triumph, having registered some impressive results since earning promotion to the Premier League a couple of years ago.
The goalkeeper added: "It's unbelievable that we are in a semi-final against Chelsea. What Swansea have achieved in the last 18 months is just a dream for the players and especially for the people who live here.
"Juan Mata is Chelsea's best player and they have just bought (Demba) Ba. They have so many players who can make a difference. But we have shown we are capable, not only with the football we play but the mentality we have.
"We are hard to beat, especially away from home. We have beaten Arsenal, Fulham and QPR in London, so that's a positive omen."