The Blues, who are currently fourth on the Premier League table, needed a win to go four points past Manchester City.
However, they failed to get the win at Gtech Community Stadium against Brentford, who held the Blues to a 0-0 draw.
As it happened
Brentford head coach Thomas Frank made two changes to his side that were beaten 2-1 away at Newcastle United on Wednesday night.
Chelsea head coach Enzo Maresca made five changes to his side that won 1-0 over Tottenham at Stamford Bridge on Thursday night.
Both teams started the game very cautiously and failed to create many chances to get the first goal of the game in the first half.
The second half also had few opportunities, as both teams struggled to get the ball into the net, ending the game in a draw.
Chelsea remained in fourth place in the Premier League table, with only two points separating them an Man City.