They surpassed the previous record of 263-5, set by Royal Challengers Bangalore in 2013
After being frustrated in the first half, Chelsea broke the deadlock in the 61st minute when Diego Costa fed Willian on the left of the penalty area and he shifted the ball to his right and curled a shot high into the corner.
Chelsea moved up to sixth in the table on 13 points while Hull are 15th on seven after a third straight defeat.