UChicago was one of my top choices when I was applying to college. Based on its reputation (its students can tell you better) it is a place where you'll work a lot. It has a trimester system like CalTech (where my younger brother is a senior right now) which ends up focusing a semester's work into a shorter period of time.
Also, when I applied, they had me go to an interview with two alumni (married) in my area. I actually did quite poorly on that interview having relaxed a little being in a private home.
And as with any other college application, the key is really to get across who you are as zephyrmaster wrote. You want the admissions board to have a good idea of who you are so they feel like they already know you. Otherwise you're just a pile of numbers and extracurriculars. I got into my first choice, Williams, on early decision though my college counselor told me it was a "reach" school by following this advice. A friend of mine who had worse grades than I did and went to a public school got into his "reach" school, Middlebury as well by doing this. With the decreasing importance of the standardized tests which were originally supposed to put applicants from all schools on the same objective scale, character rating is about the best measure schools have aside from GPAs and high school reputation.