Both sides squandered a number of clear-cut opportunities in a competitive contest, with West Ham deserving to earn a share of the spoils against their city rivals.
The Hammers remain in 17th place in the top-flight standings, while Chelsea are third and now sit two points adrift of leaders Liverpool.
Antonio Rudiger then tried his luck from 30 yards as he fired straight at Lukasz Fabianski, but for all of their pressure the Blues were struggling to create clear-cut chances with West Ham content to sit deep and wait to launch counter-attacks.
That tactic almost paid off in the 29th minute when Felipe Anderson broke down the left before playing in Michail Antonio but the attacker - in the team as a replacement for the injured Marko Arnautovic - blazed a shot high over the crossbar after getting in behind the Chelsea defence.
The near-miss only encouraged the home side and, two minutes later, a run from Andriy Yarmolenko led to Antonio getting another chance inside the area which Kepa Arrizabalaga was equal to at the near post.
West Ham's show of intent rattled Chelsea and led to the Blues taking a backwards step, but the visitors could have gone in front just before the half-time whistle only for N'Golo Kante to head a Willian cross just wide of the far post.
Both teams looked to go on the front foot at the start of the second period, with Yarmolenko curling a left-footed strike from distance marginally over Arrizabalaga's crossbar.
West Ham began to drop deeper as the second half progressed and substitute Alvaro Morata almost made the Hammers pay soon after his introduction, but the Spaniard's close-range effort hit Fabianski in the face before rebounding clear of danger.
Chelsea were dominating in all areas of the pitch but, with 13 minutes remaining, West Ham should have taken the lead when Robert Snodgrass found Yarmolenko all on his own at the back post only for the summer signing to send a free header wide from six yards out.
The visitors responded with Kante sending a first-time effort high over the crossbar from 14 yards, while Ross Barkley saw a 20-yard curler superbly tipped behind by Fabianski.
Willian also squandered a late chance from close range, and it left Chelsea having to make do with just a point against a West Ham side who are showing signs of improvement under Manuel Pellegrini.
WEST HAM UNITED (4-3-3): Fabianski; Zabaleta, Balbuena, Diop, Masuaku; Noble (Sanchez 85'), Rice, Obiang; Yarmolenko, Anderson (Snodgrass 74'), Antonio (Perez 65')
CHELSEA (4-2-3-1): Arrizabalaga; Azpilicueta, Rudiger (Cahill 69'), Luiz, Alonso; Jorginho, Kovacic (Barkley 79'); Willian, Kante, Hazard; Giroud (Morata 65')
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