After the break, the home side wasted chances to double their advantage, and Schalke made them pay when Klaas-Jan Huntelaar provided a cool finish inside the penalty area to give the German outfit a share of the spoils.
Below, Sports Mole assesses whether a draw was a fair result for the match in West London.
On target: 7
On target: 5
Was the result fair?
For the most part of the match, Chelsea dominated everything from possession to chances created, but they lacked a cutting edge in the final third to say that they conclusively deserved to win this contest. Their lack of a clinical touch in the penalty area always left Schalke in with a shout of gaining a positive result and it didn't come as a huge surprise when they equalised shortly after the hour. The home team had the better of the closing stages but they couldn't find a winning goal that would have been harsh on the Germans.
There will be aspects of Chelsea's play that Jose Mourinho will be delighted with, but it's the mistakes that he will focus on in the aftermath of this draw. In their previous performances this season, they have been ruthless in front of goal, but after easing into the lead, they seemed to fall into the trap of wanting to walk the ball into the net and it ultimately cost them three points. Hazard and Fabregas were superb, while Filipe Luis was steady on his full debut, but Mourinho will expect more from his team as they continue in the competition.
Schalke 04's performance
Jens Keller had no option but to name a mix-and-match XI for the visit to London but despite Chelsea threatening to run away with the match in the opening quarter, they acquitted themselves well and more than equalled the efforts of their opponents. Julian Draxler gave another glimmer as to why he is regarded as the next big thing in German football while Huntelaar provided a hittable target in attack. They were fortunate not to concede in the final 10 minutes but they were well worth a point in this group opener.
Sports Mole's man of the match
Eden Hazard: It was a closely-run race with Fabregas, but Hazard just about did enough to take the honours. The Belgian's final ball was off at times, but when he was given possession, he frightened the Schalke defence, who immediately retreated. Hazard is still finding his feet after the World Cup but he isn't too far away from producing his best form.
Fabregas produced another dazzling display in the heart of Chelsea's midfield, but he should have put his team in full control before half time. Branislav Ivanovic put the ball on a plate for him from 12 yards out but he somehow sent the ball high into the stands. It proved to be a costly error.
Ivan Bebek didn't have one of his best nights at Stamford Bridge. The official missed a foul by Fabregas in the build-up to Chelsea's opener and that immediately changed the course of the match. He didn't make any major mistakes for the remainder of the 90 minutes but it did take him 57 minutes to realise that Fabregas was wearing a piece of jewellery that should have been taken off before the match. It will be interesting to see how he fares in his next European fixture.
Chelsea: Chelsea's next Champions League fixture sees them travel to Portugal for their first-ever match with Sporting Lisbon.
Schalke 04: Schalke will expect to move onto four points when they host Maribor in two weeks' time.