As expected, Chelsea saw much of the ball in the opening few minutes, and Andre Schurrle flashed a shot over the bar before Diego Costa went close in the 12th minute with a measured effort from a tight angle which rolled wide of the post.
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Leicester continued to defend stoutly and, in fact, the biggest cheer of the half greeted Didier Drogba, who left his seat on the bench after half-an-hour to warm up at Stamford Bridge.
Eden Hazard was unusually subdued in the opening period, but his pass in the 37th minute almost set Costa up for the opener.
The Spanish international's low drive was turned behind by a lunging Wes Morgan as Leicester's dogged display frustrated the hosts.