Live langoustine, crayfish or prawns in Chi?
Depending on the time of year, I often see fresh langoustines at Fox & Obel. And, while I have never purchased them myself, I have generally been very happy with my seafood purchases at this store so this is where I would look first. Call, though, because I doubt that they are in season right now.
Fox & Obel
401 E. Illinois St.
As for live shrimp, well, they've been available with some regularity in a few of the Chinatown markets for the past year or so. Richwell Market, Mayflower, and Chinatown Market are your best bets.
1835 S. Canal St.
2140 S. Archer Ave.
2121 S. Archer Ave.
NB In lieu of calling I would suggest that you drop in the Chinatown shops to see for yourself...
re: Erik M
Addendum: Crawfish are currently out of season but are otherwise often available on Saturdays at Hoa Nam Market on Argyle Street. I haven't seen them on offer anywhere else in town, but, then again, I haven't looked elsewhere as I've been perfectly happy with Hoa Nam.
If you don't try tracking them down in town, though, there are a number of reliable online sources live crawfish from Louisiana during the season. I'd try Cajun Grocer for starters.