Paulinho had Barcelona’s first big chance on 16 minutes but could not direct his header from Lionel Messi’s cross towards goal.
Barcelona, who had over 70 per cent of the possession, continued to push forward and went close on 27 minute but Paulinho’s cross did not pick any teammate as Thibaut Courtois easily saved.
Chelsea won a free-kick in a good area on 31 minutes but Marcos Alonso’s well struck effort went over the wall which Marc-Andre Ter Stegen saved.
Willian should have opened the scoring on 33 minutes following a superb curler only to see his effort hit the post.
In the 41st minute Willian hit another effort but unfortunately the ball came off the post again.
Two minutes later Hazard hit a superb volley on the edge of Barcelona’s box from a poorly cleared cross which went just over the bar.
Luis Suarez had his first chance in the game on 54 minutes but his low left-foot strike from a tight angle after neatly beating Caesar Azpilicuerta was palmed away by Courtois.
Chelsea took the lead in the 62nd minute as Willian curled in a right low strike from the edge after being teed up by Hazard.
Barcelona equalised in the minute 75th minute thanks to Messi who slotted past Courtois from Andres Iniesta’s clever cut-back following careless defensive play by the Chelsea backline.
With five minutes left, Moses tried a long range effort but saw his effort go wide off the target.
The return leg comes up on March 13 at the Nou Camp.
In the other tie at the Allianz Arena on Tuesday night, hosts Bayern Munich thrashed 10-man Besiktas 5-0.
Sixteen minutes into the game, Besiktas were reduced to 10 men after Domagoj Vida was shown a straight red card.
A brace each from Thomas Mueller (43rd, 66th minutes), Robert Lewandowski (79th, 88th minutes) and a goal from Kingsley Coman (53rd minute) gave Bayern a massive first-leg advantage.