Supposedely they have free bike parking (indoor, secured):

http://www.chicagobikestation.com/

I need to leave my bike somewhere safe between 2-6 PM this Sunday. Is that place open all the time?

Also is there any safe place to park my bike in the Field Museum area , or should I not take it there? I just bough a new Dahon Folding bike so am paranoid about it getting stolen !

I'm going to send you a private message.