Juve appeared to be on course for a nine-point cushion at the top of the table when Chiellini headed them in front in the 10th minute, while they scuppered further chances to increase their lead.
Napoli then levelled just before half-time with a deflected effort and had the better chances to win the game in the second half, but ultimately had to settle for a point which maintains the six-point gap between the two sides.
Just 13 seconds were on the clock when Marek Hamsik turned Goran Pandev's cross wide.
However, it proved to be a rare threat to Gianluigi Buffon's goal as Juventus immediately gained control of the match, taking the lead in the 10th minute.
Andrea Pirlo sent in a cross from the left which was met by Chiellini, who had stayed up following a corner, and he used strength and determination to head the ball unstoppably past Morgan de Sanctis, beating Miguel Britos in the air.
Two minutes later, Stephan Lichtsteiner wanted a penalty when he went down under the challenge of Inler, but referee Daniele Orsato waved away his appeals.
Mirko Vucinic failed to replicate Chiellini's determination when he headed a cross wide of the far post midway through the first half before De Sanctis denied him with an excellent reflex save.
Napoli were struggling to get into the game, but a break in the 43rd minute saw them level through Inler. His shot took a deflection off the head of Leonardo Bonucci, which lifted the ball above the hand of Buffon.
At the end of the half, Edinson Cavani and Chiellini clashed in the penalty area with both receiving a yellow card, although the Napoli forward was fortunate not to receive more.
The home side then improved in the second half with Buffon having to earn his money.
He turned Hamsik's shot wide for a corner before parrying another effort from the Slovakian midfielder with Blerim Dzemaili sending the rebound wide.
The game then fizzled out with both sides seemingly happy with a point each, although the draw only really helps Juventus, who maintain a six-point lead at the top of the table with a superior head-to-head record over their opponents.