Chelsea scored a second successive win over a newly-promoted side when they beat Leicester City 2-0 at Stamford Bridge on Saturday thanks to second-half goals from Diego Costa and Eden Hazard.
Chelsea started the season with a 3-1 win at last season's Championship (second division) runners-up Burnley on Monday and Saturday's win over winners Leicester gave Jose Mourinho's men six points after a much improved second-half performance against the resilient visitors.
Swansea City also have six points from their opening two games after a first-half Nathan Dyer goal gave them a 1-0 win over Burnley at the Liberty Stadium.
West Ham United picked up their first points with a 3-1 win at managerless Crystal Palace thanks to two first half goals in three minutes from Argentine debutant Mauro Zarate and Stewart Downing, and a second half volley from Carlton Cole.
Marouane Chamakh scored for Palace before Cole's third for the Hammers but the Eagles have now lost both their opening games following their 2-1 loss at Arsenal last week.
In the other games Aston Villa drew 0-0 with Newcastle United and Southampton were held to a 0-0 draw at home by West Bromwich Albion.
Image: Chelsea's Diego Costa celebrates after scoring a goal against Leicester City during their English Premier League match at Stamford Bridge.
Photo: Toby Melville/Reuters