Crawford was injured in the first period of the Blackhawks' game Sunday against the Florida Panthers and did not travel with his teammates to Dallas.
Antti Raanta replaced Crawford in the 6-2 win against the Panthers and will start Tuesday against the Dallas Stars. Kent Simpson has been recalled from the American Hockey League to serve as the backup. Regular backup Nikolai Khabibulin is out with a lower-body injury.
Quenneville has no reservations about starting the rookie Raanta, who is 3-0-1 with a 2.16 goals-against average.
"Well, he's handled it well. He's been in the net. Game's been on the line, he's been solid for us. Just moving forward, you like his approach, you like his competitiveness," Quenneville said. "He's a battler. It'll be a good test for him as well."
And it's an opportunity Raanta is embracing.
"Just have to keep working hard and keep earning the minutes," Raanta said. "Even though I maybe have the No. 1 spot now, it's nothing if you go there and you're not ready to play. So you just have to keep your mind and body ready to play and keep working hard."
Kostka was activated Sunday after being sent to Rockford of the AHL on Dec. 4 and will play in his third game of the season for Chicago.
"It's good to see him. I know he played well when he went down there [to the AHL] for a couple of games," Quenneville said. "In the games he played for us, we liked what he did back there."
As for Dallas, coach Lindy Ruff has made several changes to his lines, moving Ryan Garbutt and Antoine Roussel up to the second line while dropping Ray Whitney and Alex Chiasson, who have been fixtures on the second line for much of the season, to the fourth line.
Ruff moved Garbutt and Roussel, who have combined for 10 goals, up for one simple reason.
"[I like] the speed in their game, the speed, tenacity, the fact that both of them have I think five goals now," Ruff said. "They've taken real good advantage of the offensive situations and put them in the back of the net."
And with Vernon Fiddler, who has centered the fourth line for much of the season, out with an upper-body injury that took him off the ice in the first period of a 5-1 win against the Philadelphia Flyers on Saturday, Dustin Jeffrey draws in to center the fourth line alongside Whitney and Chiasson.
Kari Lehtonen will start in net for Dallas.
Here are the projected lineups: