Cech produced several fine stops to keep the Blues in the tie as Guus Hiddink's men defended superbly throughout ahead of the second leg at Stamford Bridge a week on Wednesday.
After a cagey opening 30 minutes, in which Barcelona enjoyed plenty of possession but could not break down a solid visiting defence, the game suddenly sparked into life.
Thierry Henry cut in from the left and fired straight at Cech before testing the Blues stopper again with a much fiercer effort moments later as Barca finally began to create some openings.
But it was Chelsea who should have broken the deadlock in the 39th minute when Rafael Marquez's weak back pass allowed Didier Drogba a free run on goal but the striker's half volley was well saved by Victor Valdes, who was also equal to the Ivorian hitman's follow up.
Michael Ballack flicked a header over the bar as Hiddink's troops began the second half with more intent, while Barca were forced into a reshuffle when Marquez was forced off with a knee injury to be replaced by Carlos Puyol.
Lionel Messi, mostly on the fringes of the game, volleyed over the bar from 16 yards while Dani Alves forced Cech into another smart stop as Barca began to find their fluency again. Although a booking for Puyol for a challenge of Florent Malouda means the experienced defender will be missing for the second leg at Stamford Bridge a week on Wednesday.
Samuel Eto'o missed a great opportunity to give Barcelona the lead with 20 minutes to go when he outpaced the visiting defence but the outstanding Cech produced another excellent stop.
But the best chance of the game fell to substitute Bojan in the 90th minute when the young striker headed over the bar from close range, while moments later Cech smothered an effort from Alex Hleb as Barca ended the night frustrated and goalless - the first time they have failed to score at the Nou Camp all season.