Do I have a good shot getting into the Sloan MBA program?

I’d say you have an excellent shot. With a UChicago 3.67 GPA in a SCIENCE course (physics, chem? curious to know) you’re no doubt a highly capable person with a resume and world experiences to match. As long as your essays are as polished and pristine as your transcript (by UChicago standards…good grief that’s impressive) and your resume/recs look good, they’ll almost certainly pay you enough attention. You’re numerically qualified and so it comes down to fit, character, interview, and how you write your narrative via your application (which is a somewhat less convoluted process in the grad school context, in many ways)

Good luck and let us know of the outcome.