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The result means Liverpool will top the table at Christmas - ahead of the Gunners on goal difference - as two teams with title pretensions of their own produced a spectacle almost devoid of entertainment and quality.
Frank Lampard came closest to breaking the deadlock when he hit the woodwork in the first half, while Arsenal striker Olivier Giroud wasted two good opportunities late on to claim the win that would have seen the Gunners leapfrog Liverpool.
"Credit has to go to Blues boss Jose Mourinho for getting his tactics spot on. Chelsea crowded the midfield, had a solid defence and looked dangerous on the counter-attack. Mourinho came for a point and got one."
How Mourinho's tactics keep Chelsea in title race
Instead, referee Mike Dean's final whistle produced a chorus of boos and chants of "boring boring Chelsea" from Arsenal fans frustrated at their team's failure to lay a glove on Jose Mourinho's team.
There were some moments to debate in a match that was a niggly, messy affair played out in dreadful conditions, although arguably the biggest news of the night came further up the Seven Sisters Road where Tottenham named Tim Sherwood as Andre Villas-Boas's full-time successor.
John Mikel Obi could easily have seen a red card for a shocking first-half challenge on Mikel Arteta that went unpunished by referee Dean and Arsenal were convinced they should have had a penalty when Theo Walcott tumbled after Willian stepped on his foot just before the interval.
An undistinguished first half finally burst into life when Lampard found space on the end of Eden Hazard's clever flicked pass but saw his powerful effort bounce off the underside of the bar to safety.
The second half, if it was actually possible, opened in even more scrappy fashion and Arteta was the victim of another poor challenge from Ramires, which finally persuaded Dean to show Chelsea's midfielder a yellow card.
Mourinho made his first change with 17 minutes left, somewhat surprisingly choosing to replace Hazard with Andre Schurrle, who was soon followed into the action by Oscar, on for fellow Brazilian Willian.
Jose Mourinho is now unbeaten against Arsenal in all 10 competitive matches as Chelsea manager (all against Wenger), winning five, with five draws.
As a tortuous evening entered its final 10 minutes, Arsenal finally created a chance when Aaron Ramsey found Giroud with time and space but he sent a hopeless angled finish into the side-netting.
The France striker was then played in again at the near post by Kieran Gibbs but he was blocked by a combination of Chelsea keeper Petr Cech and his defenders.
Arsenal manager Arsene Wenger declined to make any changes when the game appeared to be crying out for the invention of Spanish playmaker Santi Cazorla - resulting in a draw that was unfulfilling for both teams.
Match ends, Arsenal 0, Chelsea 0.
Second Half ends, Arsenal 0, Chelsea 0.
Corner,  Chelsea. Conceded by Tomas Rosicky.
Attempt blocked. David Luiz (Chelsea) right footed shot from outside the box is blocked. Assisted by Frank Lampard.
Attempt blocked. David Luiz (Chelsea) right footed shot from outside the box is blocked.
Foul by Bacary Sagna (Arsenal).
Ramires (Chelsea) wins a free kick in the attacking half.
Corner,  Arsenal. Conceded by César Azpilicueta.
Attempt blocked. Bacary Sagna (Arsenal) header from the centre of the box is blocked. Assisted by Mesut Özil with a cross.
Corner,  Arsenal. Conceded by César Azpilicueta.
Substitution, Chelsea. David Luiz replaces Fernando Torres.
Corner,  Chelsea. Conceded by Per Mertesacker.
Corner,  Arsenal. Conceded by Petr Cech.
Attempt saved. Olivier Giroud (Arsenal) left footed shot from very close range is saved in the centre of the goal. Assisted by Kieran Gibbs with a cross.
Offside, Chelsea. Fernando Torres tries a through ball, but Oscar is caught offside.
Mikel Arteta (Arsenal) wins a free kick in the attacking half.
Foul by Ramires (Chelsea).
Bacary Sagna (Arsenal) wins a free kick in the defensive half.
Foul by Andre Schürrle (Chelsea).
Attempt missed. Olivier Giroud (Arsenal) left footed shot from the left side of the box is close, but misses to the left. Assisted by Aaron Ramsey with a through ball.
Substitution, Chelsea. Oscar replaces Willian.
Delay over. They are ready to continue.
Delay in match Ramires (Chelsea) because of an injury.
Substitution, Chelsea. Andre Schürrle replaces Eden Hazard.
Olivier Giroud (Arsenal) wins a free kick in the defensive half.
Foul by César Azpilicueta (Chelsea).
Attempt missed. John Terry (Chelsea) header from the left side of the box misses to the left. Assisted by Frank Lampard following a set piece situation.
Tomas Rosicky (Arsenal) is shown the yellow card for a bad foul.
Foul by Tomas Rosicky (Arsenal).
Branislav Ivanovic (Chelsea) wins a free kick in the attacking half.
Attempt blocked. Mesut Özil (Arsenal) left footed shot from the centre of the box is blocked. Assisted by Olivier Giroud with a headed pass.
Attempt saved. Frank Lampard (Chelsea) right footed shot from outside the box is saved in the centre of the goal. Assisted by Fernando Torres with a headed pass.
Attempt saved. Branislav Ivanovic (Chelsea) right footed shot from the centre of the box is saved in the centre of the goal. Assisted by Gary Cahill with a headed pass.
Theo Walcott (Arsenal) is shown the yellow card for a bad foul.
Foul by Theo Walcott (Arsenal).
César Azpilicueta (Chelsea) wins a free kick on the left wing.
Offside, Arsenal. Bacary Sagna tries a through ball, but Theo Walcott is caught offside.
Ramires (Chelsea) is shown the yellow card for a bad foul.
Mikel Arteta (Arsenal) wins a free kick in the defensive half.
Foul by Ramires (Chelsea).
Arsenal failed to reclaim top spot in the Premier League as they played out a dreadful stalemate with Chelsea at Emirates Stadium.