January in Chicago is very cold. Rains can result in intense snowfall in this month.and the temperature can go as low as 5.4 Degree Fahrenheit. So keep something very warm with you to protect yourself from the intense weather. Keep warm undergarments as well as suitable jackets and coats. It would be best if you can get a warm leather long coat for yourself, that would be ideal for outdoors.
I'd say you need a heavy and warm coat. It is very cold during this time of year a lot of snow, freezing rain and of course those high winds.