The home side finished with ten men after David Luiz was given a straight red late on for a reckless lunge at Sead Kolasinac, as the game concluded in ill-tempered fashion.
Arsenal could have sealed all three points in the second half, Shokodran Mustafi heading a Xhaka free-kick into the net only to be denied by the offside flag.
Both teams had chances to hit the front during an entertaining first half. Chelsea's best came midway through the half when Cesc Fabregas released Pedro behind the Arsenal cover but Laurent Koscielny did well to put the attacker under pressure and Petr Cech was able to parry his shot away.
At the other end, Arsenal should have seized the lead just before half-time. Aaron Ramsey's meandering run took him into the penalty area and his toe-poked shot beat Thibaut Courtois only to cannon back off the base of the post.
Alexandre Lacazette had a golden chance to bury the rebound but his first-time shot cleared the crossbar.
After the break it was an even contest, with both teams struggling to create clear chances.
Eden Hazard and Alexis Sanchez were brought on as substitutes, the former drawing a decent stop from Cech after a darting run towards the Arsenal box.
Once Luiz had been ordered off, the game descended into a series of fouls and both sides settled for their point.