EA/ED at UChicago/Brown

I recently visited the University of Chicago and Brown University and loved both. At the info sessions, I learned that UChicago only has a non-binding Early Action, while Brown only has binding Early Decision. Does applying EA/ED to either of these schools affect the probability that I will be accepted? Would it be advisable/legal to apply EA to UChicago and ED to Brown?

I can’t speak to Chicago, but at Brown it is not.

Since Chicago claims their program is “open and non binding” I believe that means you could apply to both, but if you are accepted to Brown, you must withdraw from Chicago and attend Brown.