The Hammers suffered a narrow 1-0 loss to their London rivals at the Boleyn Ground in the Premier League.
The only goal of the game came midway through the first half when Belgium international winger Eden Hazard headed home from Ramires's right-wing cross.
There were complaints of offside from the West Ham players, but the referee was having none of it.
The son of West Ham co-chairman David Sullivan, Jack, was frustrated with the decision and the final result, and made his feelings clear on Twitter.
So unlikely tonight with the offside goal, that's what happens when you play the big team !— Jack Sullivan (@jsullivanwhu) March 4, 2015
West Ham 0-1 Chelsea. The Blues remain five points clear thanks to Hazard's header. Don't you mean offside header— Jack Sullivan (@jsullivanwhu) March 4, 2015
West Ham were perhaps unlucky not to pick up a point from the match, as they did give Chelsea a run for the money.
Although Sam Allardyce’s side had 44% of the possession, they had 18 shots of which five were on target, and five corners.
Meanwhile, Chelsea had 56% possession, took 12 shots of which three were on target, and had four corners.
West Ham are currently 10th in the Premier League table with 39 points from 28 matches.