Paul Lambert's Canaries defended stoutly to record their first clean sheet since returning to the Premier League to remain ninth on the table after just one defeat in their past eight outings as Andre Villas-Boas' Blues missed a good chance to go closer to the top three despite losing just one of their last ten in the league.
Both sides were not devoid of chances although it was the visitors who looked much more dangerous but they were unable to breach John Ruddy's goal with the Norwich keeper putting in a solid shift.
Canaries skipper Grant Holt had the first real chance of the match in the 10th minute after a good build-up but dragged it just wide of the upright after taking a lovely touch inside David Luiz.
Chelsea had a great opportunity to take the lead midway through the first half when Fernando Torres cleverly shot on target with the outside of his right boot from just inside the right side of the area but Ruddy managed to put his fingertips to good use and divert it around his far post.
Bradley Johnson's 36th minute attempt from outside the box took a deflection off John Terry which forced Petr Cech to scramble but he was able to hold on and keep out a near disaster for the visitors before both keepers were called on late in the first half as Cech tipped away Holt's off-balance attempt from a bouncing ball moments before Ruddy held Juan Mata's deflected effort.
On the hour-mark, Torres' misfiring run continued when he controlled a ball from the right from Jose Bosingwa but managed to completely miss the target from just in front of the penalty spot moments before Ruddy did well to keep out Mata's angled attempt as the Blues started to look menacing.
Raul Meireles' fierce 68th shot from outside the box was not far off about five minutes before Ruddy safely held Ramires' bullet as Chelsea were doing most of the late attacking. Ruddy again came up with the goods to deny Mata's shot on the turn with a little less than 10 minutes remaining but that was about in regards to clear scoring chances as Norwich grabbed a well-deserved point in front of their loyal home fans.
Carrow Road, Norwich - 26,792
Yellow cards:NOR - nil CHE - nil