Paille, who was acquired last season in a trade with the Buffalo Sabres, posted 10 goals and nine assists for 19 points with a minus-4 rating in 74 games for the Bruins. He was a mainstay on the Bruins' penalty kill.
"When we acquired Dan I think he really helped shore up our penalty killing and he brought us speed to the lineup, to the forward group, and he also was able to play up and down the lineup," Chiarelli said.
A first-round pick by Buffalo in the 2002 draft, Paille has scored 45 goals and added 96 assists in 269 career games.
Paille appeared in all 13 playoff games last season. Boston eliminated Buffalo in six games then won the first three against Philadelphia in the Eastern Conference semifinals before dropping the next four.
The Bruins are not expected to aggressively chase free agents.
"I don't really have any pressing needs from purely acquiring someone on the free-agent market, so I don't think you'll see much from us in the next couple of days," Chiarelli said in a conference call with reporters.
On June 22, the NHL's second lowest scoring team last season obtained forwards Nathan Horton, Florida's leading scorer since he was drafted in 2003, and Greg Campbell for defenseman Dennis Wideman and two draft picks. Four days later, the Bruins drafted 18-year-old center Tyler Seguin with the second overall pick with expectations that he would contribute as a rookie. And two days after that, they re-signed 42-year-old Mark Recchi for one season.
Now Chiarelli plans to monitor the market before deciding whether to make any trades.
"If there's not something in the trade market, I would say, yes, I'm probably done shopping," he said.
"I think we can get them back in the mix. It might be a little tight," he said.
Meanwhile, he's waiting to decide on his own unrestricted free agent forwards Miroslav Satan, who had five goals and five assists in the playoffs, and Steve Begin. He said he told their agents he may renew talks at some point.
Chiarelli spoke to several general managers and said trades remain a possibility.
"We'll let the market shake out a bit [and] pick up those conversations again," he said.
"There will be intense competition. That's the way we had planned it," Chiarelli said. "I'm comfortable with it [but] I'm not saying it's going to end up that way."
Joe McDonald covers the Bruins and Red Sox for ESPNBoston.com. Information from The Associated Press was used in this report.