If you’d have no regrets going to University of Chicago, if it is truly your first choice school, give it the ED app. Then it’s game over. You are set at s top school. You have given yourself the absolute best chance if admissions with that ED application there. But that means foregoing CalTech and MIT acceptances if they happen EA.
Otherwise EA all three schools and add some safety schools, some rolling admissions State schools and other EA schools so that you have your safeties in place to focus on the RD round if deferred at all 3 top choices. I suggest Tulane, UMichigan as a couple of strong EAChoices. Gives you a litmus test on how competitive a candidate you are in the early round.