The draw leaves Arsenal second in the table, with Chelsea in fourth and Liverpool will be top at Christmas.
The first real chance came after 32 minutes, when a delicate Eden Hazard chip found Frank Lampard at the far post. He met it with a controlled volley which beat a rooted Wojciech Szczesny, but the ball crashed against the underside of the bar and bounced out.
Arsenal had two key chances in the closing stages, both to Olivier Giroud. The first came after a delightful dinked ball from Ramsey, which the Frenchman ran onto, but his shot skewed to the left of the goal.
The second came five minutes from time as Kieran Gibbs crossed low from the left and found Giroud but his effort was blocked by a combination of Petr Cech and John Terry. Cesar Azpilicueta then cleared a Bacary Sagna header off the line in the final few minutes as Chelsea got the draw they came for.
PRE-MATCH: A couple of slightly surprising elements to those teams. No Mathieu Flamini for Arsenal, with Tomas Rosicky getting the nod ahead of him, and presumably Aaron Ramsey will therefore take up a more central role. And for Chelsea, Ramires plays in a slightly more advanced role, and may well start on the left to try and combat Theo Walcott's pace, while Willian is a slightly surprising inclusion ahead of both Oscar and Juan Mata.
32' - CHANCE FOR CHELSEA Ooof - Lampard goes incredibly close. A beautiful ball over the top from Hazard finds Lampard at the far post, and his volley smacks against the underside of the bar. Chelsea can't convert the rebound, and Arsenal clear.
44' - CHELSEA COUNTER-ATTACK: Ramsey plays himself into some trouble and an errant pass sets up a Chelsea counter. Hazard breaks down the left, he lays it off to Willian but his shot is low and weak and not a problem for Szczesny.
78 - BIG CHANCE FOR ARSENAL: Ramsey dinks the ball over the top for Giroud, but under pressure from the advancing Cech, he skews it wide. Should have scored there.
85' - SO CLOSE FOR ARSENAL: Rosicky feeds Gibbs on the left of the area, Giroud gets to his low cross but a combination of Cech and Terry gets the ball over the bar.
90+1' - OFF THE LINE: Ozil swings over a corner, it finds Sagna but his header is cleared off the line by Azpilicueta.
Arsenal had 62% possession, Chelsea 38%
Arsenal only had two efforts on target, the first coming in the 85th minute.
Chelsea had 13 shots, nearly twice that of Arsenal, despite their dominance of possession.
TALKING POINT - Mourinho sets Chelsea up for the point. It was clear from relatively early on in the game that Chelsea and Jose Mourinho were more than happy with a point, just as they were when they visited Old Trafford early in the season. It was enough to frustrate Arsenal, who despite having the majority of possession, suffered from the 'sterile domination' that Arsene Wenger has spoken about many times before.
MAN OF THE MATCH
John Terry (Chelsea): Arsenal only had two shots on goal, and a big part of that was the Chelsea captain, who capped a fine performance by denying Giroud in the closing stages.
ARSENAL: Szczesny 5, Sagna 6, Mertesacker 5, Vermaelen 6, Gibbs 6, Arteta 5, Rosicky 6, Ramsey 5, Ozil 6, Walcott 6, Giroud 6.
CHELSEA: Cech 6, Ivanovic 6, Azpilicueta 7, Cahill 7, Terry 8, Mikel 6, Lampard 6, Ramires 7, Willian 5, Torres 5.
SUBS: Luiz 5, Oscar 5, Schuerrle 6.
MATCH IN A TWEET