The Blues were not at their best against Arsene Wenger’s men who always looked to be the more likely side to steal the three points.
After a bright start from Chelsea, Arsenal soon took control of the match and Danny Welbeck headed an effort just wide before Alexandre Lacazette and Sead Kolasinac tested home keeper Thibaut Courtois.
Pedro looked lively for the home side but was unable to cause any real trouble for former Blues keeper Petr Cech while Alvaro Morata could only head a chance wide as Chelsea struggled to find the match’s opening goal.
At the other end, Granit Xhaka and Laurent Koscielny both fired wide before an Aaron Ramsey effort struck the post and Lacazette blasted a chance off target when easier to score as the half ended 0-0.
The second half saw Chelsea struggle to create goalscoring opportunities and other than a couple of half chances for Willian, The Blues had little to show for their efforts.
Arsenal thought that they had grabbed a winning goal 15 minutes from time but Shkodran Mustafi saw his headed effort ruled out for offside.
Eden Hazard and Cesc Fabregas then missed further chances to score for Chelsea before David Luiz was sent off three minutes before the end for a late challenge on Kolasinac as the match ended goalless.
The goalless draw represents the first time in which Chelsea have failed to score at Stamford Bridge under manager Antonio Conte’s leadership.