Maurizio Sarris side had won all five of their opening Premier League fixtures before their trip to the London Stadium on Sunday.
But Chelsea struggled to find a way past West Hams stubborn defence and were forced to settle for a point following a goalless draw.
Jorginho, meanwhile, continued to be the metronome at the heart of Chelseas midfield.
And the £57 million summer signing set a new Premier League record by registering 191 touches during the game – which is more than any other player since records began in the 2003/04 campaign.
Jorginho had held the previous record alongside Manchester Citys Fernandinho when he registered 186 touches in Chelseas 2-1 win over Newcastle United last month.
The Italy international also attempted 180 passes against West Ham – an average of one every 30 seconds – which is more than any other player since Premier League records began.
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