Chelsea's perfect record in the Premier League came to an end on Sunday, while Arsenal once again got the better of Everton at The Emirates Stadium..
Maurizio Sarri's side, seeking a sixth consecutive win, dominated possession but came up empty in a goalless draw at West Ham United.
The Blues now sit third in the table, two points back of perfect Liverpool and behind champions Manchester City on goal difference.
"This was not our best performance," said Sarri.
"I knew West Ham is a very good team.
"We aren't happy with the result."
Arsenal made it four league wins in a row by beating Everton 2-0 with goals from Alexandre Lacazette and Pierre-Emerick Aubameyang.
Petr Cech came up with several key saves in posting his first clean sheet as the Gunners pushed their home unbeaten run against the Toffees to 25 games.
"I think 20 times maybe, Cech kept us in the game," Aubameyang said.
"I think we are improving every day and feeling good and better, so when we win it is better for the team."
Despite West Ham seeing little of the ball in the first half at the London Stadium, Michail Antonio had two good chances but came up short on both.
Chelsea's Alvaro Morata came on after the break and got right into the action with a chipped shot that hit spread-out Hammers keeper Lukasz Fabianski in the face.
West Ham's Andriy Yarmolenko then squandered the game's best chance by sending a free header wide in the 78th minute and Fabianski ably handled two final Chelsea chances.
The Hammers remain in 17th place, but took a point for the second straight game after losing their first four.
"It was a good point against the leaders and a team that scored 14 goals in the first five games," manager Manuel Pellegrini said.
"I am happy with the performance and if you cant win, then draw."
Arsenal had to work at the Emirates Stadium in continuing their domination of Everton.
The Gunners were sluggish in the first half and were only level thanks to Cech, who made saves against Theo Walcott, Lucas Digne and Richarlison.
Arsenal finally came to life in the 56th minute when Lacazette cut into the area and curled a shot in off the far post.
They doubled their lead three minutes later when Aubameyang finished off a three-on-one attack with Mesut Oezil and Aaron Ramsey, though replays showed him to be offside.
Cech then preserved the shut-out with late saves against Michael Keane and Cenk Tosun.
"The result doesn't reflect what both teams played," Everton boss Marco Silva, whose club is 12th in the table, said.
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