Juve - Serie A winners for the last three seasons - have not been crowned European champions since 1996, with their best recent effort a quarter-final appearance in 2013.
However, with Massimiliano Allegri's side the sole Italian represenatatives in the competition and leading their domestic league by nine points, Chiellini says now is the time for Juve to impress.
"Our group is strong and has grown steadily over these past few years. Now we also want to show how far we've come on the European scene," he told Rai.
"We must approach the Champions League with enthusiasm but at the same time be aware of the responsibility we have in flying the flag for Italy in Europe."
Dortmund visit the Juventus Stadium in improved form, having won their last three Bundesliga games to climb to 12th.
Despite a troubled start to the campaign, including a number of key injuries, Jurgen Klopp's men are now seemingly on the up - something that has not escaped Chiellini's attention.
"Anything can happen in two games of football. Dortmund have welcomed back important players whose injuries have contributed to the first half of their season," he added.
"We have great respect for them, but also a strong desire to win, go through and keep our European dream alive. We feel stronger and more mature than in previous years.
"The risks are their counter attacks and pace. They have players who thrive in space, although by aiming for pace they also take great risks and leave themselves exposed.
"This was seen in the first half of the season, when they conceded many goals by leaving huge gaps."
