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.
The Championship outfit held the Premier League champions to a stalemate at Carrow Road, earning a replay at Stamford Bridge for a second chance to make it into the fourth round of the competition. We knew the difficulty of the game.
The first half was an unforgettably forgettable one, with neither keeper being properly tested.
The west Londoners have lifted the trophy four times in the last 11 seasons and they'll be confident of seeing-off Norwich in the third round of the competition this year.
They now face a replay in London to add to a busy January, which also includes a two-leg League Cup semi-final against Arsenal.
"When a striker plays he wants to score, but I'm pleased for his commitment and his work for the team".
"It's a pity because we wanted to win the game, instead we have to play another game".
Norwich responded with their own attack and nearly took the lead from a 70th minute free-kick which was punched away by Caballero with Murphy's followup volley hitting a Blues player.
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.
"We have to play another game - the schedule is busy. The only problem we have is Hazard because he had a kick in his calf and he has to try to sort this problem". For our fans and our club a really good moment. Maybe in the first half we could be better. Here's how we predict Chelsea will lineup.