Usually you don't just approach strangers and start talking, unless you're in a bar or a social club. That can be perceived as weird here. Although , you can have varying degrees of success with it depending on how attractive you are (I know, the world is unfair).

Have you considered joining something like the Rotary Club, or the Fraternal Order of the Eagles? Those types of groups are all about fraternization and accomplishing goals together.

Chicago is a big baseball town. You could learn about baseball and go to a game. You probably won't meet anyone at a game, but it'll get you pumped up about the sport. Baseball is pretty boring until you attend a game. Once you've been to the ballpark and felt the energy, the game will suddenly click for you. Then get yourself a Cubs hat and start going to a sports bar on game nights. It's completely appropriate and common to talk to people there. Cheer together about the game. Complain loudly about the umpire, and bond with your fellow fans. After attending a few times you'll start to recognize people who show up regularly. They won't all drink, btw, so that doesn't need to be a concern. You can exchange contact information with people you get along with. Heck, find a decent sized group of friends there and offer to be a designated driver. That will immediately earn you some popularity points and people will be calling you every week to see if you want to carpool to the game.