if they need any help from an intern, even if it is not paid? A lot of these firms are busy and maybe they could use some help? I am sure if you contact the HR Department, they will say no since you are not in an official hiring time. Instead, you can find lawyers' emails on the firm's website. I would email a copy of your resume to some of them and simply offer to help them immediately since you already have prior experience and live in Chicago. Tell them you will work for free, just for the experience. Maybe it will open something for the summer.
Unfortunately I am not in a situation where I can work for free. Fortunately I have a few callbacks for 1L SA gigs (due in part to some help from an NDN poster) so hopefully things go well.