The MS funding makes it trickier... Stipend and tuition? UChicago is a great place, so I hear. Still, I would have my reservations. Are you supposing that the MS will strengthen your application towards top ten PhD programs? It might, but I would be wary of that mindset. Ask your professors what they think about this matter... From what I've gleaned, MS applicants are held to a different bar. Without striking research, you'll be facing difficult competition. Cultivating research in a MS program can sometimes be a challenge, though, as your grad studies will be intense.
There's also the issue of classes. Entering a PhD from a MS likely means repeating a year of courses... You may be able to skip some, but I hear it is rare to bypass all the core courses, even if you've taken them. Again, the first two years of a PhD in the US is essentially a MS degree. By completing the MS first, you may be extending your number of years as a student.
All this in mind, I would be hard pressed to forfeit the PhD offer from UIUC. If you're concerned about the prestige of UIUC vs. Harvard or Princeton or whatnot, then, well, I understand. Those schools have established a brand name for themselves that carries clout. But prestige isn't the cornerstone of academia. It's research! You'll likely find some theorists whose work sparks your interest at UIUC, and you'd be advancing your career at a top institution.
Anyway, either route will likely be successful, but as far as career tactics go, I would say the MS route is less clear and more time-consuming than the PhD one. Worst case scenario: after the MS, you'll hopefully be admitted to a strong PhD program, but it may not be as highly ranked as you would have hoped. You still would have a strong MS degree under your belt in case you bail on the PhD, and you would have lived and learned in Chicago. Best case: you kick butt in the MS program and get admitted to your dream schools later. The downside is you're spending more time as a student.