The OP's thinking is screwed up in a number of ways, but the one most easily corrected is the OP's incorrect assumption about aid. While it is true that a number of colleges give out aid essentially on a first-come, first-served basis, that's not even remotely the case at Chicago (or indeed any of the top private universities). If you are an American citizen or permanent resident -- and that's an important "if", because it doesn't work this way for international applicants -- the university will offer you a financial aid package that meets 100% of your "need" (as they, not you, calculate it), whether you are accepted EA in December or taken off the waitlist in June. There's really no difference based on when you are accepted. They also offer merit scholarships of varying amounts that are not based on "need", and those are carefully doled out between people accepted in the early and regular rounds, mostly to people who don't otherwise qualify for need-based aid.
The most common result of an early application is getting deferred until the regular round. If that happens to the OP, he or she should not assume it means that there won't be any financial aid. On the other hand, the OP should clearly do some research to figure out what a 100% need package will look like in the OP's circumstances, so he or she can figure out whether that will be do-able.