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Young Frenchman David Faupala was on target with an equaliser which gave City hope at the break.
Experience told after the restart though with Chelsea putting four second-half goals past Willy Caballero.
There was encouragement despite the result, with Tosin Adarabioyo earning the man-of-the-match award and three local lads being on the pitch at the same time in the second half. Watch all the action above.