In a closely fought encounter at Dagenham & Redbridge's Victoria Road ground, a second half header from Blues striker Sebastien Kneissl was all that separated the two sides.
Once again, Hammers coach Roger Cross was forced to field an extremely young line-up who did well against their more experienced opponents. With just eight first team starts between them - earned by Stephen Bywater, Anton Ferdinand and Youssef Sofiane - the hosts were up against it facing a Chelsea side containing two players who had appeared in the World Cup Finals - Celestine Babayaro and Mario Stanic - and a back four that most Premiership first teams would be happy with - Babayaro, Robert Huth, William Gallas and Mario Melchiot.
Against that kind of defensive rearguard, chances were always going to be at a premium for Hammers, but our back three of Ferdinand, Phil Lumsden and Darren Blewitt, and impressive 16-year-old wing-back Chris Cohen, ensured that the Chelsea attack were kept just as quiet at the other end, and the first half ended without either side having created any clear-cut chances.
Blues midfielder Filipe Oliveria came close with a long-range effort that Bywater tipped on to the post, and the Hammers keeper had to be alert to keep out a similar effort from Melchiot just before the interval, but that was the nearest they came to taking the lead.
The game opened up in the second half and, boosted by their impressive first half performance, Hammers began to push forward with more confidence. Trent McClenahan headed just wide at the far post, while Sofiane burst clear on the right but saw his low shot blocked by Chelsea keeper Neil Sullivan.
Just when it seemed as though Cross's team were beginning to get a grip on proceedings, though, the visitors struck what proved to be a 64th minute winner. Babayaro found space on the left and delivered a dangerous cross that was headed firmly past Bywater by Kneissl from 10 yards out.
It was a blow that Hammers failed to recover from and Chelsea's superior passing quality ensured that they played out the final stages without facing any threat to their lead.
Hammers: Bywater, McClenahan, Cohen, Ferdinand, Lumsden, Bunce
(M Noble 69), D Noble, McMahon, Pearson, Sofiane. Subs unused:
Forde, Laws, Carrick, Wright, Lee.
Chelsea: Sullivan, Melchiot, Babayaro, Gallas, Huth, Nicolas,
Oliveria, Boussoufa (Tillen 66), Kneissl (Jeffreys 82), Keenan,
Stanic. Subs unused: Pidgeley, Rocastle, Grant.