That replay is likely to be played in about 10 days' time, stuck-in between the Leicester City and Brighton games, a week before going back to the Emirates for the second leg of the League Cup semifinal.
Chelsea came out with more objective in the second half and had a chance on 50 minutes but Angus Gunn got down well to smother Michy Batshuayi's long-range shot. Now we have to play another game at Stamford Bridge and Norwich deserved this opportunity, another chance.
Chelsea were abysmal in the first half, but looked slightly brighter when they came out after the break.
Chelsea did improve after half-time, with Willian injecting some much-needed pace and drive around the box.
Norwich made one change as Zimmermann replaced Oliveira.
It's claimed that David Luiz considered a move out of Chelsea in November after falling out with the manager, but in the end it was the club owner's wish that prevailed.
Mourinho blasted Conte's behaviour during their match at Stamford Bridge in October 2016
Chelsea pressed late on but the closest they came to a victor was when Davide Zappacosta shot narrowly wide in injury-time.
Conte admitted that he was disappointed with the result and extra game to add to their already busy schedule, but also acknowledged that Norwich were worthy of the draw. When you play in this trophy you know it is very hard, but today the commitment of my players was very good.
If Chelsea were trying to win, we sure weren't reflecting that attitude on the pitch, especially in a beyond dire first half.
Antonio Conte used Saturday's clash as a chance to give some of his squad players more game time, but it backfired as they struggled to create openings and will need a replay if they are to progress. We found a bit of difficulty we tried to win the game.
"Don't forget that Michy is a young player".