The visitors began brightly but could have been behind in the 31st minute had goalkeeper Kepa Arrizabalaga not denied Michail Antonio from four yards out.
“We knew Chelsea would have a lot of the play, as they have all season, but to create the chances we created, that’s what let us down. All round it was a fantastic defensive performance; the way the lads dug in, fought together and stayed together got us a deserved point. We’ll take that all day long“, said Mark Noble, West Ham captain.
Alvaro Morata, who came in in the second half of the match created great chances for the blues but was unable to convert one for the team.
A point drops West Ham to 17th on four points. Chelsea move down to third, level on 16 points with Manchester City.
They have a difficult match ahead on 29 September, hosting league leaders Liverpool.