The left side of Navy Pier is lined with parking garages. There's one with a sign that says Chicago Shakespeare that'll get you very close! Make sure you have your parking validated for a discount if you see a show as well. :)
Show your ticket to parking attendant if you have and as stated in other answers you'll be directed to a dedicated parking area, don't forget to take parking ticket in for validation. Oh yes it's the closest parking to theatre. Enjoy!
There is parking on the pier. Chicago Shakespeare has dedicated parking for people attending their productions. The entrance is just past the Riva turnaround. Tell security you're here for Shakespeare and they should allow you through even if the lots are full.
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