The Blues, who secured emphatic 6-0 wins over West Bromwich Albion and Wigan Athletic in their first two games, found no difficulty in overcoming Stoke at Stamford Bridge.
England midfielder Frank Lampard had a first-half penalty saved by keeper Thomas Sorensen before being substituted after picking up a hernia injury.
Florent Malouda made amends in the 32nd minute when he latched onto a defense-splitting pass from John Terry to open the scoring.
Didier Drogba wrapped up the win on 77 minutes when he converted a penalty awarded after Nicolas Anelka was fouled by Sorensen.
Manchester United and Arsenal remained two points behind the Blues after defeating West Ham and Blackburn Rovers respectively.
United claimed a 3-0 victory over West Ham, thanks to goals from Wayne Rooney, Nani and Dimitar Berbatov.
Arsenal won 2-1 at Blackburn with goals from Theo Walcott and Andrei Arshavin.