United held away to Southampton.
Southampton held Manchester United to a 1-1 draw at St Mary's yesterday afternoon.
A deflected Che Adams shot gave the hosts the lead on the half-hour mark, before Mason Greenwood equalised just after the half time break.
Romelu Lukaku was on target for Chelsea on his debut, in their 2-0 win away to Arsenal.
Reece James got the second goal for Chelsea, who made it 2 wins from 2.
Tottenham also have six points thanks to a 1-0 away to Wolves - Dele Alli scored a first half penalty, while Harry Kane came off the bench in the second half for his first appearance of the season.
Tonight, West Ham take on Leicester City at the London Stadium from 8.

Thursday Morning Sports Update
Former Liverpool And Blackburn Full-Back Inge Bjornebye Joins Rangers As Football Consultant And Advisor
Lizzy Kent Appointed FAI's New Head Of Women And Girls Football
No Afternoon Session At The PDC World Darts Championship Today
Wednesday Morning Sports Update
Tuesday Morning Sports Update
Niall Kelly Retires From Inter County Football
Boxing Promoter Frank Warren Revealed Potential Fight Between Anthony Joshua And Tyson Fury