Gunners boss Arsene Wenger is now without a win against Jose Mourinho in his last 13 encounters.
The goalless draw marked the first match in which Arsenal have failed to score at home this season.
Chelsea remain first in the Premier League following the draw while Arsenal joined second placed Manchester City on 67 points but have a game on mind.
The Blues only need six points from their remaining games to clinch the league title but Arsenal still have a mathematical chance to win the championship.
Mesut Özil started for Arsenal and completed more passes (76) than any other player in the game and also had the highest pass accuracy at 93 percent.
The 26-year-old completed more dribbles (5) than any other player in the game and had the highest rating on the Arsenal team according to Whoscored.
Arsenal – Chelsea
Referee: Michael Oliver
Kick-Off: 16:00 GMT
Ospina, Bellerin, Mertesacker, Koscielny, Monreal, Coquelin, Cazorla, Ramsey, Özil, Alexis, Giroud
Subs: Szczesny, Debuchy, Gibbs, Wilshere, Walcott, Flamini, Welbeck
Manager: Arsene Wenger
Courtois, Ivanovic, Cahill, Terry (c), Azpilicueta, Matic, Fabregas, Ramires, Oscar, Willian, Hazard
Subs: Cech, Filipe Luis, Zouma, Mikel, Loftus-Cheek, Cuadrado, Drogba
Manager: Jose Mourinho