Cristiano Ronaldo set up Mario Mandzukic's winner in a 1-0 victory over Valencia in Turin that ensured Juve will finish Group H in the top two.
In a season where Juventus are expected to challenge for multiple honours, Chiellini was delighted to see Massimiliano Allegri's men achieve their first objective of 2018-19.
"The first goal of the season has been reached," he said in quotes published on Juventus' official website.
"We knew that it would be a difficult game because Valencia are a dangerous team in the spaces.
"In the first half we could do better, we got too enthusiastic, then we did well in the second [half] - the result is certainly deserved."
Manchester United's dramatic late winner against Young Boys means Juventus have not yet secured top spot in the group, though they hold a two-point advantage ahead of their trip to Switzerland on matchday six.
It is a tricky run for Allegri's men, who have an eight-point cushion at the top after 13 games.
"Now we turn the page and start thinking about the Champions [League] in February," Chiellini added.
"We have to concentrate on the championship because we have a good month ahead of us."