The Turin outfit finished nine points clear of Napoli in Serie A last season, but the Italian has refused to get carried away with their favourites tag.
"History dictates that winning three consecutive championships is very difficult," Chiellini told the club's official website.
"We've got everything required to do it, but it won't be a walk in the park. After all, it wasn't a straightforward run to the title last year, given that the gap in the table was minimal in January.
"Then we did well to motor along stronger than the others when people thought we might have paid the price for our involvement in the Champions League."
Chiellini made 31 appearances for Juve last season.