Manager Maurizio Sarri started his Blues reign with five straight Premier League wins – but they could not maintain the record against a battling Hammers side.
And in the end Chelsea were grateful for Andriy Yarmokenko’s glaring second-half miss, when he headed wide with only keeper Kepa Arrizabalaga to beat and the goal at his mercy, for not suffering their first defeat.
The visitors had chances of their own, with West Ham keeper Lukasz Fabianski saving well from substitutes Alvaro Morata and Ross Barkley – but in the end a draw was a fair result in a game that rarely sparked into life.
It is a result that drops Chelsea into third place behind Manchester City on goal difference and leaves Liverpool two points clear at the top of the table with a maximum return from their six games.