The Gunners could not break down Roberto Di Matteo's side in a match which failed to really spark at the Emirates Stadium, with both sides lacking quality when attacking
Chelsea's 1-0 victory over Barcelona in the Champions League had evidently taken its toll on the starting XI involved in that match as Roberto Di Matteo made eight changes to his team.
The Blues were still able to hold their own, however, and frustrated the Gunners for the most part despite lacking a touch of class in attack that may have enabled them to take more than one point from the game.
Chelsea will have their sights focused on the second leg of their European semi-final and the upcoming FA Cup final but the stalemate does give Tottenham, who have a game in hand, the chance to pull four points clear of Roberto Di Matteo's team in the race to finish in the top four.
Arsene Wenger looked to add some spark to his side following their disappointing 2-1 loss to Wigan by introducing Alex Oxlade-Chamberlain into the side in place of Yossi Benayoun, who was ineligible to feature against his parent club. Aaron Ramsey replaced the injured Mikel Arteta while Laurent Koscielny and Kieran Gibbs returned to the back four.
The Chelsea changes included the introduction of young left-back Ryan Bertrand ahead of Ashley Cole, while Fernando Torres replaced Didier Drogba in attack, with the Ivorian left out of the squad entirely.
The Blues looked happy to sit back and absorb pressure in the early stages when Arsenal gained possession but looked sharp and threatening when they sprung out of their compact defensive shape to attack.
Torres nicked the ball away after some diligent defensive work in the Arsenal half on a couple of occasions but despite moving the ball well in midfield Chelsea could not take advantage in attack. Salomon Kalou half-heartedly appealed for a penalty after he had lost control of the ball when through on goal on the left-hand side, but it was correctly waved away.
The home side slowly grew into the game, though, and wasted a golden chance to take the lead after 14 minutes. Theo Walcott guided a superb free-kick towards the back post that dropped into the lap of Robin van Persie but the Dutchman could only stab his finish wide from point blank range.
From there, the first half petered out. Arsenal struggled to find fluency in midfield, with Ramsey guilty of coughing up possession on more than one occasion, while the Chelsea front three of Kalou, Torres and Daniel Sturridge could not conjure up anything in the final third that worked Wojciech Szczesny.
Petr Cech remained similarly untroubled until the Gunners carved out a flurry of opportunities as the half drew to a close. Koscielny was entirely unmarked when he headed a Van Persie free-kick against the crossbar before the Dutchman controlled Alex Song's excellent pass to force Cech into a good block inside the penalty area.
That brief respite in an otherwise tepid affair was not, unfortunately, a sign of things to come in the second half. The first 15 minutes comprised of a collection of incomplete crosses, mistimed through balls and, in defence of the two sides, reasonably solid defending.
Walcott was hauled off just after the hour mark after pulling up with a hamstring injury that was handled in a way that will not have pleased Stuart Pearce, England's interim manager, who was in attendance.
The forward attempted to play on after appearing to suffer a tweak to the muscle and only seemed to risk aggravating the problem before he again went down in pain and was substituted minutes later.
Gary Cahill appeared to lean on Van Persie when challenging for a high ball in the penalty area but referee Dean remained unmoved despite the striker's protests, while despite substitute Juan Mata's best efforts, he could not instigate much of an improvement in Chelsea's invention levels in the Arsenal half.
Van Persie began to find more space as play became more stretched in midfield but could not take advantage, wriggling away from a couple of Blues defenders and a stranded Cech in the box only to see his shot blocked by the keeper.
Koscielny had to be alert to slide in and prevent Sturridge from shooting from close range at the other end as the moment of decisive quality needed to give either side the edge did not come.
Commentaries, Stats, Player Ratings and much more,
Visit Goal.com Live Scores!