Juve, last crowned champions of Europe in 1996, play host to the Ligue 1 club on Tuesday in the first leg of their quarter-final tie and defender Chiellini is confident of his side's chances of going all the way.
"I think Juventus is improving its European performances comparing to the previous years," said the 30-year-old.
"This group of players is more confident and is ready to achieve something important at an international level.
"Then obviously we need to show that on the pitch. But again we have the feeling that we can do very well in this competition, better than what we did previously."
Monaco are into the last eight for the first time since 2004, giving Chiellini and his team-mates plenty to be wary of.
He added: "Monaco have a good mix among players with international experience and young players that are showing their full qualities in the last period.
"They are back playing important games like these recently, and I think that this year they have found that confidence that allowed the team to perform constantly at very high level.
"If you look at their results in Ligue 1 you can see they have the best defence, and even more important looking at the record they had in Champions League in the group stage and what they did in the last 16, we can say they are the real surprise of the competition."
