Better look into renting, because if your cyc is stained, not just dirty, there's no guarantee it will come clean, and even if it will, I doubt you ca get it done in time. I don't know anyone in Chicago that cleans soft goods but try contacting either
Reed Rigging Reed Rigging Inc.
or The Chicago Flyhouse,
Chicago Flyhouse Inc
2925 W Carroll Ave
· Chicago
· (773) 533-1590
I don't think either of them does the cleaning, but they will probably know if anyone in the Chicago area does do that.
If you get something cleaned it will also need to be retreated afterwards since you'll likely be washing off all flame retardants. Just keep that in mind too