Chicago is NOT a cheap place to live. If you live there already and are not paying rent, you could get away with the budget you're proposing. All the same, if it's $22k per year, that's $44k over two years, and I don't know anyone who can survive on $3k a year (based on your estimate of $50k total debt, or even $8k, based on your calculation of $60k) in Chicago. Please remember that you have to factor in things like insurance and food, as well as transportation. I got into UChicago a couple of years ago, and declined the offer. I calculated that it would cost about $100k for the degree (AM). Thankfully I had a good offer at Boston College, so it made the decision easier. I grant that there are lots of great folks at UChicago, but as with everything else, it depends on what you're looking for. It might be wise to see if you could get in touch with students who are currently in the program to see what their budget is like (most students get 50% tuition). Best of luck in your discernment!
P.S. Most of my friends have been devoting about $20k to living expenses (rent, utilities, insurance, transportation, food, books) in Boston, and I'd imagine that the figure would be somewhat similar in Chicago (I lived there for four years, and it's slightly less expensive there, depending on where you live).