I know Chicago is the "Windy City" but is it too windy to play badminton on the beaches?

I think, it's almost always pretty windy near water but BCoughlin is right, it's possible to pick a сalm day and enjoy a game in fresh air. But I like playing indoors anyway. It's guaranteed you'll have no disturbing wind)) Check out http://trytopic.com/ the game I organize is listed there

First, it's called the "Windy City," because of a World's Fair over 100 years ago where Chicago was a bit too boastful in proclaiming the city as the greatest in the world. So it's not really directly related to the wind gusts in the city. That said, it can get awfully windy some days when you're close to the lake. I'd say half the time you'll probably struggle a bit to play badminton, as the birdy will move around quite a bit. You'll have to pick your days, but there are definitely times you won't contend with too much wind and have a successful game.