I'm an alum of the graduate division, but please, allow me to share my insights.
Based on the evidence available (LSN graphs, personal anecdotes) attending a particular institution for undergrad has a marginal effect at most, if there is an effect at all. I enjoyed reading an M.I.T. discussion on the matter, and trust me, they are dealing with the same kind of angst and cynical jealousies that the students at U of C deal with during the law school admissions process. As it turns out, the law school admissions cycle is primarily economics at work: It is in the school's best interest to report a high GPA, regardless of how that GPA was acquired or where. It is also in the school's best interest to lie about grade trends and difficulty in major as relevant considerations, as doing so assists them in getting as many applicants as possible (only to axe them two months later). In fact, from an economics standpoint, it is downright irrational for schools NOT to be handing out fee waivers to people they believe would not have applied had it not been for the "free chance". Virginia is doing it right if you ask me. The take away point from all of this: Imagine the most cynical scenario you can rather than the rosiest. This will lead you in general, and in law and economics particularly, to the right answer to your question more often than succumbing to wishful thinking.
If you earnestly believe that having "The University of Chicago" on the diploma behind your desk and on the resume you give to employers will help you, then let the system/society/business culture decide if that optimism is correctly informed. As a personal matter, if I am hiring someone and I see the University of Chicago on a person's resume, barring they were on athletic scholarship (haha, jk) and/or got under a 3.0, I would certainly be inclined to give preference to their case. That is because I am a human, and as such, I am inclined to caving toward my biases. In law school admissions offices, as they are run presumably by humans, the bias-effect is also at work. Having said that, these people have in most cases been trained to look at two numbers and two scholastic numbers only: GPA and LSAT, and even to OVERLOOK numbers such as an abnormally low first LSAT at times. Since the "University of Chicago" is an institution, (and a damn good one at that), it should not in theory (based on schools admitting students for ranking purposes) affect the admissions process in the affirmative or negative. In reality, the theory is nearly proven with exceptions every now and then.
There. Good luck to all of you. I personally have tremendous respect for U of C undergrads. I find that you guys are on average almost as intelligent as the U of C graduate students, which is a major compliment.
An aside: My colleague (a uchicago UG alum with a 3.92 GPA in history) is applying to law school this cycle and he didn't ace the LSAT (a 166), but is faring well as you can imagine.