Massimiliano Allegri's men have struggled to get going in 2015-16 and Sunday's 2-0 win over Genoa was only their first league victory of the season.
Juventus have already fallen eight points behind leaders Inter in the Serie A table, but Chiellini is determined to keep fighting until the very end.
"This win will add to our growing confidence and we'll see where we are come May," Chiellini told the official Juventus website.
"Inter lead the way at the moment but the league doesn't finish in September.
"That tenacious streak has never left this side, it's still there for all to see.
"We'll take each game as it comes. After this week we have plenty of belief going forward for the rest of the campaign."
Juventus already recorded a 2-1 Champions League win over Manchester City in midweek and Chiellini was pleased to see them build on that win versus Genoa.
"Before Tuesday, we knew that a good start in the Champions League would get us going and rekindle that spark that was lacking in our first three league games," he said.
"We've come to what is a very difficult place to play against a typically fired-up Genoa side and left with an important three points. We read the game well and grew into it after the first goal."