I agree with the others but with some caveats.
If you want to match in Chicago, you should be able to do that. You have a solid app, you are from there, and Chicago has a variety of tiers of programs, so I would feel pretty good at matching somewhere in Chicago. I think doing an early Sub-I at your school and getting honors will likely benefit you more than an away rotation. Getting some good letters of rec will also really help.
Now, to talk more generally about away rotations. As mentioned above, away rotations are not necessary for IM, so I would not recommend doing them except for the following reasons:
1) Geographic necessity: If you need to be at a certain program due to geographic limitations, then an away rotation can be helpful. But, I am talking about really legitimate reasons (sick family members, spouse's job), NOT just because you really want to live there or end up there. However, this really only applies to programs in places where there is only one or two programs, and if you really need to be in that location.
This does NOT apply to places like Chicago, NYC, Boston, Philly, etc where there are a bunch of programs (with a variety of competition levels). So, you do not need to do a rotation for this reason.
2) Breaking into the next tier of competition: As mentioned above, you have a pretty solid app, and you have a great chance of matching somewhere in Chicago. However, if you really have your heart set on the upper tier (maybe Northwestern or UChicago), then an away rotation may give you that extra boost your app lacks. Plus, if you do an away rotation, you are likely to get yourself an interview at the program. This may not greatly increase your chances of matching there, but your chances are certainly improved over not interviewing at all.
This second approach is risky, and I wouldn't count on it working out. But it is always worth a shot if you are set on the upper tier. I would not recommend it unless you are really sure and you think you can show up and do well.
I do want to end with saying that you (and everyone) needs to be really careful with away rotations in specialties where they are unnecessary. I would NOT do an away rotation at a place where you are already very competitive (except for reason #1 above) because I think you are more likely to do poorly or do nothing to improve your application (which can be just as bad). For you OP, I think you are probably competitive at several Chicago programs, so you really don't need to do an away rotation.