The home side had the better of the chances, but were lethargic and poor on the ball throughout, with Chelsea largely containing them with ease, though showing little ambition themselves.
Clearly fearing the effects of his players of having played two huge semi-finals in the past week and with the second-leg against Barcelona to come on Tuesday, Roberto Di Matteo made eight changes to the Chelsea lineup.
Only Cech, Terry and Cahill remained from the side that battled to secure a 1-0 lead over Barca on Wednesday.
Yet despite the rejigged lineup, it was Arsenal that started slowly. The Gunners allowing Chelsea too much space in midfield and allowing gaps in-behind their defense.
Chelsea adopted a similar approach to the one that gave them success against Barcelona; happy to sit-back and strike on the counter.
And, although Chelsea looked dangerous when they went forward, perversely it was Arsenal that ahd the two best openings of the first half. Robin van Persie really should have given the home side the lead when he arrived free at the back post from a free-kick. But electing to go with the outside of his left-foot, the Dutchman could not direct it back toward the goal and it went behind.
As the game picked up in intensity toward the end of the opening period, Laurent Koscielny came agonizingly close to breaking the deadlock. Again from a free-kick, the defender was completely unmarked, but his header bounced back off the bar with Cech unmoved.
The second-half went much the same way. Arsenal continued to be incapable of breaking down Chelsea's midfield and defense, while the Blues failed to take advantage of some promising counter-attacks. Van Persie looked the man most likely to break the deadlock, but his finishing proved unusually wayward.
Both managers will have to garner more inspiring performances from their sides if they are to achieve the goal of champions League qualification next season. But Di Matteo will likely be the happier, given how many changes he made to his lineup.
Arsenal remain in third place in the Premier League, seven points ahead of Chelsea, albeit having played a game more.