There were some surprising omissions form the the Gunners' squad as Alexis Sanchez was left on the bench, while Mesut Ozil was not included in the squad.
After a quiet start to the half, the visitors had a chance to break the deadlock when Alexandre Lacazette broke through on goal, however the striker sliced his effort horribly wide.
Clear cut chances were hard to come for both sides and they were restricted to efforts from distance, none of which were threatening.
That proved to be the trend for the rest of the half as the sides went into the break goalless.
10 minutes into the second half, Alvaro Morata tried his luck from 25-yards but the Spaniard's strike was palmed away by David Ospina.
Arsenal were dealt a blow a minute later when Jack Wilshere was forced off with an injury and replaced by Mohamed Elneny.
With the Gunners pushing for an opening goal, Arsene Wenger introduced Alexis Sanchez for Lacazette.
Chances were few and far between in the second half, but the game livened up in the final 10 minutes at Stamford Bridge.
With two minutes remaining, the woodwork came to Arsenal's rescue when Cesc Fabregas' cross took a deflection and crashed against the upright.
That proved to be the final chance of the half as the clash ended goalless at Stamford Bridge.