The Blues scored in just the fourth minute when Demba Ba controlled a long ball over the top before laying back to the onrushing Brazilian, who found the bottom corner with an accurate outside-of-the-boot effort.
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Ten minutes later Ba almost made it two when he fired at goal from a narrow angle, forcing John Ruddy into a smart save at his near post.
Ruddy then almost gifted the Senegalese frontman a second when he rushed off his line and misjudged the ball. Fortunately for the Englishman, Ba scuffed his shot and Sebastien Bassong was able to rush back and clear.
Norwich had their first decent chance midway through the half when Ricky van Wolfswinkel drove a low cross that looked destined to pick out Jonny Howson until Petr Cech diverted the ball over the bar.
David Luiz almost doubled the visitors' advantage in outrageous fashion on the stroke of half time when his effort from at least 40 yards landed on the roof of the net.