Chilwell equalised in the 76th minute, to cancel out Michail Antonio's opener just after the hour mark, and then turned provider for Kai Havertz's winning goal two minutes from time.
But the Blues still had to survive a late Hammers rally, with the visitors convinced they had levelled the game at 2-2 late on through Maxwel Cornet after Chelsea keeper Edouard Mendy had weakly palmed the ball away having dived a the feet of Jarrod Bowen.
But Cornet's effort was ruled out after a VAR check ruled Bowen's trailing leg on Mendy a foul in the build-up.
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