With Manchester United climbing to the top by virtue of their 1-0 victory over Liverpool earlier in the day, the Gunners needed all three points to return to the summit.
It was somewhat surprising then that Arsene Wenger opted for a 4-5-1 formation, leaving Emmanuel Adebayor to forage alone in attack and, more surprisingly, Robin van Persie on the bench.
The Dutchman had return from a two-month lay off with an impressive performance against Steaua Bucharest in midweek.
Arsenal had the lion's share of the game in the opening quarter but the closest they came was when Alex looped a defensive header over his own goalkeeper but, fortunately for him and Chelsea, the ball bounced wide.
Chelsea, without the injured Didier Drogba, opted for Andriy Shevchenko as their solo point of attack and Avram Grant's side often played on the counter-attack.
Manuel Almunia had one save to make from a 25-yard Shaun Wright-Philips shot.
There was nothing else to test the Gunners keeper in the first half hour until a vicious swerving shot from Shevchenko forced the him to pat the ball away for a corner.
Tomas Rosicky woke Petr Cech from his slumbers on 38 minutes with a drive from the right that whistled just past his right post.
John Terry hobbled off with an ankle injury on 40 minutes, but although the Gunners seemed to turn the pressure up another notch, there was little to show for their efforts in the final third.
However, with seconds remaining of first-half injury time, Gallas made the most of a rare error from Cech when he rose highest to head home a Cesc Fabregas corner after the Chelsea keeper had let it pass through his grip.
Arsenal had to thank Almunia just before the hour when he parried a well struck goal-bound shot from Shevchenko and then got up well to save the rebound across the other side of his goal.
Grant then brought on Claudio Pizarro for Claude Makelele and switched to a 4-4-2 formation.
However, his side were showing their frustration at chasing the game and the scything tackles began to fly in.
Joe Cole only received a yellow card for a two-footed lunge at Emmanuel Eboue, who himself was stretchered off the pitch.
That enforced change meant that the Gunners also altered formation to mirror that of the visitors.
Substitute van Persie tested Cech within seconds of taking the field with a left-foot low drive from the left side of the area that the Czech keeper found too hot to handle.
But fortunately for him, the Gunners did not have anyone following up and at the other end Arsenal successfully played out time.