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Both goalkeepers made important saves to preserve the draw at the Camp Nou, with Victor Valdes making a reaction save on a shot from Didier Drogba following a Barcelona defensive lapse in the 39th minute.
Chelsea goalkeeper Petr Cech dove to keep Samuel Eto'o's shot out in the 70th after the Barcelona striker had shook off Alex to get a clear chance from close-range.
The English club is the first to hold Barcelona scoreless since the Spanish league leaders lost to Numancia 1-0 on the opening day of the season.
Bojan Krkic headed a clear chance from point-blank over and Cech came out to block fellow substitute Aleksandr Hleb's dangerous opportunity - also in injury time - as Barcelona pressed following Eto'o's chance.
Eto'o had run into the area before pulling back to shake off Alex, but Cech kept the low shot out at the near side.
Barcelona coach Pep Guardiola left captain Carles Puyol on the bench and a defensive error nearly cost the host team late in the first half.
Drogba jumped on Rafael Marquez's poor backpass for an attempt from inside the area but the Chelsea striker couldn't control the rebound from Valdes, who poked the ball away before the danger was cleared.
The chance seemed to rejuvenate the Blues, who had spent most of the first half holding off the rushes of Barcelona's talented forwards, with Andres Iniesta creating most of the danger.
Lionel Messi's hesitation in the 10th allowed Chelsea to clear the ball away, and he would have few clear chances as Florent Malouda and Jose Bosingwa - filling in for the suspended Ashley Cole - kept the Argentina winger in check, with Messi only managing two high shots from outside the area.
Barcelona held most of the possession - just as it did in big wins over Lyon and Bayern Munich - but Chelsea's defense held well, especially after having allowed five goals in the previous round against Liverpool.
Cech was busy throughout as he smothered Henry's chance in the 31st and blocked a hard shot from the France striker two minutes later.
It was the two clubs fourth meeting in five European campaigns, and things heated up as the fouls mounted.
Barcelona had a major blow in the 50th when Marquez pulled up with a left knee injury that will keep him out for the rest of the season, making way for Puyol.
Barcelona's defense will be short-handed for the return leg at Stamford Bridge on May 6 with Puyol suspended after being booked in the 74th.
