Connor Murphy scored, and Marc-Andre Fleury made 29 saves for the Blackhawks (16-22-7), who have lost six of their past seven games.
"It's a crazy game, especially on my side," Chicago coach Derek King said. "First few shifts, we couldn't handle pucks, we were giving them away. We settled in and we were kind of in it, but we made a couple mistakes and they capitalized, (which) seems to be our M.O. We don't have that luxury of making two or three mistakes. We have to play a pretty solid hockey game, and we were just flat at times. We had a few pushes, but we were a little flat.
"I think they're trying. I really do believe we're trying. Sometimes they don't try the right way, if that makes sense. They work hard at times, and then sometimes, they don't work smart. And I'll keep pushing it on them, I'll keep sending the message that we have to play a certain style of hockey to be able to at least have a chance to win a hockey game."
Chiasson, who played his 600th NHL game, gave Vancouver a 1-0 lead at 12:21 of the first period with a wrist shot from the slot. It was his fifth goal of the season.
"Pretty special," Chiasson said. "I think today I had a moment just to realize a lot that I've been through. I've had a lot of people supporting me throughout the process. This isn't just about me. I'm thankful for them. This is the greatest game to play. I've had the opportunity to win (the Stanley Cup) in Washington. I think that kind of keeps you open-minded on things.
"I've had the opportunity to play with some of the best players in the game. This game has given me so much. I just feel really grateful for these opportunities and now being part of this group."