Serie A leaders Juventus are flying high at the moment after Saturday's 2-1 win over Udinese and are still unbeaten in the league this season with 12 wins and eight draws from 20 matches.
However, despite their dominant performances, Chiellini insists the Bianconeri have to be wary of 12th-placed Parma on Tuesday, and in particular, the threat of Giovinco, who used to play for Juventus after graduating from the youth ranks.
"Parma are a great team at home," Chiellini said on the club's official website. "Giovinco is the star and we know him well.
"It will be important to be able to regain our energy levels, because we're playing every three days and this will continue until the [Coppa Italia] clash with AC Milan."
Chiellini did however admit that confidence at Juventus is at an all-time high at the moment, as the Bianconeri have emerged as genuine title contenders under coach Antonio Conte this season.
"We're performing beyond the best possible expectations," the defender added.
"We were convinced that we'd be able to enjoy a great season, but we were also coming off the back of two difficult years and a lot changed in the summer.
"We've done well to find an immediate balance and an identity of playing. Now we're continuing to develop.
"It's a process that hasn't stopped yet and must continue if we want to be able to achieve a dream."
Juventus are a point ahead of Milan, who travel to Lazio on Wednesday evening.