The Swans will return to Premier League action after the two-week international break with an away game against the Blues.
Garry Monk's side have made a strong start to the 2014/15 campaign with four wins from four competitive matches, including a 2-1 victory over Manchester United at Old Trafford on the opening day of the season.
Chelsea have also won all three of their league games, but Fabianski believes that Swansea can get a result at Stamford Bridge on Saturday.
"It's a big game to enjoy, not to fear," said the 29-year-old. "Playing away at Chelsea is always difficult but we don't have to be afraid of anyone.
"We went to Old Trafford and won on the opening day of the season so we know we can compete with the best teams.
"If we keep our discipline and take our chances the way we have been, then anything is possible.
"It's a shame the international break came when it did because we made a great start to the season with three wins from three.
"That puts you off but the manager has kept the pressure on us to keep working hard. We've done well so far, but it's only the start and we have a tough match coming."
Fabianski has been in impressive form for Swansea since joining the Welsh outfit on a free transfer in the summer after his contract with Arsenal ran out.
The Poland international goalkeeper has conceded just one goal in four competitive matches this season and hopes to keep a clean sheet at Chelsea.
"I'm really enjoying my football here and that shows on the pitch," added the former Legia Warsaw shot-stopper. "But that's only natural when things are going so well.
"We're very pleased with the defence so far. I'm working closely with Ashley Williams and we already have a good understanding.
"We know what we expect from each other and we haven't been giving opponents much of a chance.
"I'm sure it will be different at Chelsea with the talent they have in attack but we're targeting four wins from four games."