In Chicago, all you need is a Library card. With anybody's name on it.
I am speaking from my own personal experience.
My daughter was registered in Des Plaines and going to school in Chicago. On election day she told me she had voted. I told her she should have stopped by the house, since she was in the suburbs and I wasn't working that day. She replied, "no, Dad, I voted down here in the city."
http://www.elections.il.gov/Downloads/ElectionInformation/PDF/registervote.pdf