Last season they made it to the final before harshly falling to rivals Arsenal.
The replay at Stamford Bridge will take place in the week of January 15.
The Blues come in to the game off the back of a thrilling 2-2 draw with Arsenal at the Emirates on Wednesday night which means they're unbeaten in their last seven games in all competitions [W5 D2 L0].
The Brazilian saw a couple of shots saved by Gunn and also picked out Drinkwater with a low cross from which he fired wide.
Norwich showed promising signs in the early exchanges without every worrying Caballero, only a misunderstanding between the goalkeeper and Luiz threatening to break the deadlock.
Chelsea made nine changes, with David Luiz making his first appearance since November 22 and Batshuayi, Caballero and Kenedy starting. We dominated. They didn't even have one shot on our goal and we had chances to score.
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Kyrgios had earlier battled back from a set down to beat Alexandr Dolgopolov 1-6 6-3 6-3 on Friday to book his spot in the semi-finals.
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Chelsea pressed late on but the closest they came to a victor was when Davide Zappacosta shot narrowly wide in injury-time.
"Today it was a bigger chance to beat Chelsea than in the away game, but we will try everything", he said.
Antonio Conte: "For sure there is a bit of disappointment because to have another match in a schedule so busy is not easy, is not simple, but we tried to win the game". When you play in this trophy you know it is very hard, but today the commitment of my players was very good.
Norwich have been eliminated in all four previous FA Cup ties against Chelsea, most recently in the fifth round in 2006-07.
"Don't forget that Michy is a young player".