I might be in the minority here, and I don't want this post to offend - but as a husband and aspiring grad student, I feel I can relate to your situation.
However, I can't speak to your specific circumstances. I can say that there's no way I'd personally ever consider a LDR with my
wife while I attended graduate school. My wife also works in a specific industry that's limited to certain areas of the country. This was one of the very first things I discussed with her when I decided an MBA was something I wanted to pursue. Where could she find a job she liked? Where would she happy living? I then tailored my school selections with that in mind. It sounds like you're well past that point now (congratulations on your Chicago admit - a serious accomplishment).
While from the information you've given, it seems like your spouse is being pretty close minded about find a new job in a city the size of Chicago, it also seems a bit unfair to me to uproot her a third (!) time, because
you applied to a school in an area she wasn't interested in going. If she told you she was ok with it, and then changed her tune once you were admitted - I'll retract that as it changes everything.
As my wife and I plan for a move to NYC from a suburb of Dallas, it's becoming pretty clear that this is going to be a lot harder on her than it is on me. She's leaving a job she loves to be thrown into a big city she's unfamiliar with. I'll be surrounded by like-minded students and opportunities to meet new people. She has no guarantee of finding a job she'll enjoy - where as I basically show up and I'm set. She'll continue working while I (potentially) have a life-changing experience. And a few years later I'll probably uproot her again as I pursue full-time employment.
In closing, if I were you, and you couldn't convince your wife to move to Chicago (and bear in mind, you'll likely be moving again after graduation unless you decide to stay in and find a job in Chicago), I wouldn't attend. There's always next year - and there's no way I'd jeopardize my marriage over two years of schooling, when a little compromise would let me have my cake and eat it too. Maybe not what you wanted to hear, and much longer than I anticipated - but hopefully some useful perspective for you. Best of luck with your decision!