Chicago has a vibrant triathlon scene centered on the Chicago Triathlon race in August - one of the largest triathlons in the country. The local Ironman is really Ironman Wisconsin up in Madison, though it's not that far to the similar in time frame Ironman Kentucky in Louisville.
Open water swim training - you've got Oak Street Beach on Lake Michigan, and hopefully a wetsuit. For long runs, the Chicago Lakefront path is perfect for training, as are other trails in the area such as the Des Plaines River trail. Biking gets a little trickier, and it depends where in Chicagoland you are. The general rule is to get away from the city as far as possible - in some cases, that means WIsconsin!
The Chicago Tri Club keeps a race calendar here: http://www.chicagotriclub.com/atraces/RaceList.aspx?sMode=1