From the Chicago Tribune:
Here's the expected timing:
Snow will increase in intensity and become heavy at times south of Interstate Highway 80 Tuesday afternoon, gradually spreading north into northern Illinois by Tuesday evening.
Snow--at times heavy--will continue Tuesday night into Wednesday morning. Snow showers will continue near Lake Michigan in northeast Illinois Wednesday morning, shifting into Northwest Indiana during the afternoon.
Northeast winds of 25 to 40 mph with stronger gusts are expected to result in blizzard conditions developing Tuesday evening and continuing into the overnight hours.
Light snow is expected to fall starting Monday morning with up to 4 inches of accumulation expected by midday Tuesday. Following that, the more severe storm is expected to move north into the Chicago area from Arkansas late Tuesday and into Wednesday.