Arsenal were seeking to build on their successes over the Premier League champions in last season's FA Cup final and August's Community Shield, but they began the match with Alexis Sanchez among the substitutes, while Mesut Ozil -- who Arsene Wenger said was nursing an injury -- missed out on a place in the squad entirely.
There were clear chances for both sides in the first half, with Danny Welbeck heading wide for Arsenal and Chelsea's Pedro unable to take his chance when through on goal.
Arsenal had the majority of the chances though and might well have had the advantage shortly before the break, but Aaron Ramsey was denied by the post after keeping his balance in the area to fire off a shot, with Alexandre Lacazette failing to hit the target from the rebound.
Antonio Conte made a defensive change at half-time, bringing on Tiemoue Bakayoko for Pedro, which allowed Chelsea to gain greater solidity.
Arsenal thought they had made the breakthrough when Shkodran Mustafi headed past Thibaut Courtois, but the defender was flagged offside. At the other end, Chelsea substitute Eden Hazard threatened the Arsenal goal when he found space on the edge of the area, but his shot could not beat Petr Cech.
Chelsea went down to 10 men in the 88th minute when Luiz -- already on a yellow card -- was shown a straight red for a dangerous challenge on Sead Kolasinac.
It was the third successive meeting between the teams in which Chelsea had seen a man sent off, with Victor Moses and Pedro Rodriguez having been dismissed in the FA Cup final and Community Shield respectively.