Both sides were left to rue missed first-half opportunities in a match between two London rivals that failed to catch fire until the Brazil defender received his first-ever Premier League red card with three minutes remaining.
The Gunners had the better of the opening half and should have gone into the break ahead when Aaron Ramsey hit the post and Alexandre Lacazette somehow fired over from the close-range rebound.
Chelsea had earlier missed a one-on-one opportunity from Pedro, who was foiled by Petr Cech.
The second half lacked the excitement of the first and the introductions of Eden Hazard and Alexis Sanchez from the two substitutes' benches did not provide the desired spark.
And David Luiz saw red for a high challenge on Sead Kolasinac as the game neared its conclusion, marking the third straight match Chelsea have had a player sent off against Arsenal and rounding off a poor performance from Antonio Conte's men.
Chelsea's run of five straight home league wins over Arsenal is ended by the draw, which leaves the champions three points behind Manchester City.
Arsenal have now won just two of their first five league games this season. The point means they remain three adrift of their rivals and six off Manchester City at the top, having gone 14 matches without beating a top-six team away from home in the top flight.
Chelsea threatened first with both Pedro and Cesc Fabregas forcing former Blues goalkeeper Cech into early action.
Arsenal responded with two swift passing moves, Danny Welbeck heading wide to conclude the first before Hector Bellerin, the creator of both opportunities, fed Lacazette to force a good low save from Thibaut Courtois.
The Gunners threatened again when Kolasinac's 20-yard drive tested Courtois, who parried to safety, but it was the hosts who should have been ahead when Pedro was played in on goal by a superb Fabregas throughball, only to send his shot too close to Cech.
The intensity of the match slowed as the first half progressed, but Granit Xhaka's 25-yard drive narrowly missed the target and Arsenal then missed a golden chance to take the lead just before half time.
After collecting a pass from Iwobi, Ramsey kept his footing in a solo run to beat Cesar Azpilicueta and David Luiz, before digging out a shot that struck the inside of the post, with Lacazette firing the rebound over when it looked easier to score, a miss that left the Arsenal bench looking on in disbelief.
Conte brought on Tiemoue Bakayoko for Pedro, who had taken a knock, at half-time and Willian fired an effort at Cech as the Blues looked to make a fast start after the break.
But the second half was not producing the same attacking action as the first, resulting in Arsenal making their first change with 24 minutes remaining, Sanchez replacing Lacazette, with Chelsea promptly responding by introducing Hazard in place of Willian.
The Gunners then suffered a blow when Welbeck was lost to injury, Olivier Giroud coming on, but the substitutes could not liven up proceedings.
Arsenal did have the ball in the net when Shkodran Mustafi headed in, but the defender was well offside when Xhaka played in his free-kick.
Hazard cut inside and fired at Cech at the other end, but a disappointing second half did have a dramatic sting in the tail when David Luiz lost possession and jumped in high on Kolasinac as the Blues ended another match against Arsenal at a numerical disadvantage.
Key Opta stats:
- This was Arsene Wenger's 59th match versus Chelsea with Arsenal, making them the club he’s faced the most often during his time at the Gunners.
- Chelsea failed to score in a competitive home match under Antonio Conte for the first time (27 games).
- The last time that they failed to net in a competitive game at Stamford Bridge was back in April 2016 against Manchester City (0-3) under Guus Hiddink – 29 games ago.
- This was the first 0-0 draw between these two sides at Stamford Bridge since April 2005 and the first time that Chelsea have failed to score at home against the Gunners since then, after 12 successive home games with a goal versus them.
- Arsenal have now failed to score in eight of their last 14 trips to Stamford Bridge in all competitions.
- This is the first time that Arsenal have failed to score in as many as three of their opening five league games in a season since 1998-99 (also three).
- Chelsea have now been given six red cards in the Premier League against Arsenal – their joint-most against a single opponent (along with vs Liverpool, Man Utd and Everton).