Definitely allium. Some folks dig and replant the bulbs. You're in Chicago, we never had a problem overwintering in the ground in Columbus, Ohio. USDA zones/weather patterns are somewhat similar. We always left our bulbs in the ground and got a grand display of 4' tall purple flowers every summer. Haven't grown them in years, ours were older Globemasters.
It's a Fall bulb, to be technical but if someone gifts you some I'd go ahead and stick them in dirt and wait for results next year. Same as starting with bulbs planted this fall, bigger bulbs=bigger plants.
