Italy defender Chiellini opened the scoring 10 minutes into his first start since suffering a calf injury in December, only to see it cancelled out by Gokhan Inler's deflected long-range strike two minutes from half-time.
The draw means champions Juve move up to 59 points with 11 games left while Napoli have now drawn four games in a row.
Home striker Edinson Cavani, who has not scored in six games, was lucky to escape a red card for an apparent elbow on Chiellini late in the first half but could be punished by Serie A on video review next week.
Chiellini sparked the incident, in a high-pressure game where Napoli fans had pelted the Juve team bus with stones before kick-off, by pulling the Uruguayan's hair.
"I think we shown how much we want to win the league this year," Chiellini told Sky Sports Italia.
"We're happy with our performance and it's a shame that we didn't win as we hoped to, but it was the right result.
"It [my calf] still hurts. I have to thank the medical staff. We've worked into the night every day and even at home. "I'm happy to have helped the team today, even if I know that I have to improve physically."
INCREASINGLY SLIM
Following the clash between Chiellini and Cavani, referee Daniele Orsato decided to book the pair after consulting his goal-line official.
"You can see what happened from the video, but at the end of the day it's right that we have a good go at each other and the referee decides. After the match it's all over," Chiellini added.
Juventus manager Antonio Conte was keen not to lose his temper in front of the cameras again after his two-week ban for criticising officials in January.
"Giorgio was looking to see what kind of gel Cavani was wearing," he joked.
"It was a test of character and despite the fiery atmosphere we kept our cool and we were always in the game.
We're six points ahead... but there are still 11 games left in which we have to go to Inter and Lazio and have Milan at home and next week we have to take on this season's revelation, which is Catania. Every match can bring surprises."
Chiellini, 28, had Andrea Pirlo to thank for his goal after he powerfully headed in a pearl of a cross from his Italy and club team-mate.
Walter Mazzarri's side reacted well to going behind and pushed Juve back but struggled to create clear-cut chances against a defence well-marshalled by Chiellini.
Juve were dangerous on the break and Mirko Vucinic should have twice extended their lead soon after the opener.
First he headed narrowly wide after another great cross, this time from Arturo Vidal, and then he shot straight at Morgan De Sanctis when put clean through on goal again by the Chilean.
Juve paid for their wastefulness when Inler's effort was deflected by Leonardo Bonucci's head over Gianluigi Buffon And into the net.
Napoli had the better of the play in the second half but were restricted to shoo
