The Turkish champions managed to peg back Jose Mourinho's Blues at the Turk Telekom Arena in Istanbul thanks to Aurelien Chedjou's second-half goal but scoring away from home will certainly please the 2012 European champions.
Chelsea found themselves ahead early through Fernando Torres and had a couple of other chances throughout but will have to settle for an impasse ahead of the return bout at Stamford Bridge on March 18.
The opening goal for the visitors came inside ten minutes when Andre Schurrle played Cesar Azpilicueta down the left before the Spaniard cut back for compatriot Torres to score with a simple side foot after opening his body.
The goal did nothing to drown out the noise of the fervent Galatasaray fans as they spurred on their side which was being led by former Blues star Didier Drogba and Wesley Sneijder - both of whom experienced plenty of success under Mourinho.
Roberto Mancini's Cimbom were able to respond 20 minutes into the second half when Sneijder's inswinging corner from the left found Chedjou inside the six-yard box for the Cameroonian to volley home past Petr Cech.
Earlier, however, there were opportunities created by both sides particularly when Cech got down to his left to glance Selcuk Inan's long range effort past the far upright.
Seven minutes into the second half and it was Fernando Muslera's turn to deny the opposition when he threw out a hand to thwart Torres' angled attempt from close range.
Minutes before the equaliser, Galatasaray had a golden opportunity when Drogba won the ball in the air only to see Inan inexplicably miss the target at the back post.
After the leveller, Chelsea were all about controlling the tempo of the contest and despite the best exertions of the home side, managed to hold out for a draw which has them in a fairly comfortable position for the return bout.
2013/14 UEFA Champions League - Round of 16 first leg
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