There was one change on either side from their last encounters, as Michail Antonio replaced the injured Marko Arnautovic for the Hammers, whilst Willian replaced Pedro.
The first chance went to Chelsea with Willian's out-swinging corner finding the run of Olivier Giroud, who miscued a volley from 12 yards on nine minutes.
Buoyed by their Europa League win in Greece, the Blues fashioned another chance on 12 minutes after Eden Hazard and Willian combined on the edge of the box.
The West London side received a big opportunity as Felipe Anderson deceived Cesar Azpilicueta to play Antonio behind the defence only to rush and sent the effort over the crossbar from 14 yards out.
Andriy Yarmolenko managed to break forward before being eased out by David Luiz, but the ball fell to Antonio who was superbly denied by Kepa Arrizabalaga at the near post.
In added time, Willian's first-time volleyed cross found the run of the French midfielder Ngolo Kante who sent a glancing header just wide of the far post.
After scoring with a cut inside from his left foot last weekend, Yarmolenko nearly did the same from further out but the well-struck effort sailed marginally over the crossbar.
A big opportunity for Chelsea came as Luiz got on the end of another superb delivery from Willian, but the defender could only send a free header high over the crossbar from 12 yards on 55 minutes.
Change on 65 minutes happened for both sides as Alvaro Morata replaced Giroud for Chelsea, while Lucas Perez came on for Antonio for West Ham.
The Hammers edged closer every time to steal a win, as Yarmolenko narrowly nodded a cross by Robert Snodgrass wide on 77 minutes.
Time was running out for the Blues and substitute Ross Barkley tried to be the match winner in added time but a finger-tip from Lukasz Fabianski kept him out.
Earlier, it was Kante coming close to breaking the deadlock but after appearing goal-side, shot high and wide of target to share the spoils.