I think this is an FA Cup game where we could see a shock.
After Chelsea brought on Alvaro Morata for Michy Batshuayi - who struggled all game - Norwich responded by bringing on Oliveira as they looked to nick a late victor.
Daniel Farke's side are thirteenth in the Championship standings, with 34 points from 26 games.
That ultimately proved to be Chelsea's last chance of the game.
Chelsea's line-up included only two of the team which started against Arsenal on Wednesday night, Gary Cahill and Tiemoue Bakayoko, which meant a rare...
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Norwich made one change as Zimmermann replaced Oliveira.
Chelsea continued to press in the early part of the second half and were close again but were again denied by Gunn who dived low to keep out Willian.
Five minutes after the restart, Batshuayi finally recorded a shot on target, but the Belgian striker's effort from distance lacked power and Angus Gunn had no trouble gathering.
Chelsea did improve after half-time, with Willian injecting some much-needed pace and drive around the box.
With 16 minutes remaining, Conte replaced the misfiring Batshuayi with Alvaro Morata, but even his first-choice striker was unable to provide a victor.
"David Luiz is ready and will be in contention".
Charly Musonda and Davide Zappacosta went close late on, but Chelsea failed to deliver the outcome Conte would have wanted as they add a replay to their already busy schedule.