Brentford striker Ivan Toney, bidding for inclusion in Gareth Southgate's World Cup squad, kept the Chelsea defence busy and had his best opportunity in the ninth minute, forcing Kepa Arrizabalaga into a leaping save to tip the ball over.
Winger Bryan Mbeumo should have put Brentford ahead early in the second half but his point-blank shot went straight to the in-form Chelsea keeper.
At the other end the visitors' attacking efforts were limited and lukewarm. David Raya saved a skidding shot from Chelsea captain Cesar Azpilicueta in the first half and batted away an on-target effort from Kai Havertz in the 69th minute.
Graham Potter's side finished strongly, substitute Christian Pulisic forcing Raya into a stinging save in the last five minutes, but Brentford held on for the draw. .