The Blues came close to opening the scoring early on, when Eden Hazard hit the bar.
Here, Sports Mole takes a closer look at the events that unfolded at Stamford Bridge.
On Target 8
On Target 1
Was the result fair?
Chelsea completely dominated from start to finish and will consider themselves extremely unlucky not to have won this evening. The visitors came into this game with a defensive mind-set and never looked like troubling their opponents. The Blues had 37 attempts on goal, but due to a combination of poor finishing and good goalkeeping from Adrian, they were forced to settle for a point.
Jose Mourinho's men had 72% of the possession and a host of chances, but could not break through a stubborn West Ham backline. They were frustrated by a side that had everyone behind the ball and found it hard to get in behind the defence. Chelsea may be left ruing their inability to have made the most of their chances if these two dropped points prove to be crucial in deciding the title.
West Ham's performance
The Hammers were set up by Sam Allardyce to defend this evening, and they will have impressed their manager by clinging on to a clean sheet at Stamford Bridge. They managed only one shot on goal all evening, and saw little of the ball, but their determined performance will have delighted their fans, and proved that they are up for the challenge of a relegation battle.
Sports Mole's man of the match
Adrian: West Ham keeper Adrian was inspirational this evening, and was crucial in his side keeping a clean sheet. He tipped Hazard's early effort onto the bar and blocked close-range strikes from Terry and Eto'o in the first half. After the break, he continued to keep Chelsea at bay, and in the final minute of stoppage time, he was alert to block a strike from Lampard and earn his team a point.
We may have been talking about a famous West Ham win, had Andy Carroll not made such a mess of a shot in the second half. He was picked out at the back post by Stewart Downing, and with just the keeper to beat, he completely missed the ball. It may be harsh to be so critical of him after months out injured, but a striker of his quality should have done much better in that situation.
Neil Swarbrick handed out four yellow cards for deserving fouls, and got the big calls correct. He had an awkward moment at the end of the game, when Eto'o thought the keeper had wrongly placed the ball for a free kick and ran in to score, but he rightly disallowed the strike.
Chelsea: The Blues face league leaders Manchester City at the Etihad Stadium next Monday.
West Ham: West Ham welcome Swansea City to Upton Park on Saturday.