Conte replaced the sacked Gigi del Neri this week.
"I did not have the fortune to play alongside Conte, but I am very curious to see how he does. He is a person who brings enthusiasm and determination," said Chiellini.
"The fans called for him to be hired, but that is not the only reason the club called Conte. The supporters are important, but it's wrong to think the directors follow their whims. This decision was carefully considered."