Those airports are a pain, even for a highish speed IFR medevac.
Quite a few also require you to reserve a slot for timing. Ohare is a "high density" airport, so off hours is your best bet, and they can, and will, turn you away if they are busy.
I flew a 207 into that area and ended up just going into Exec (KPWK).
I fly a 208 into ORD daily (with the exception of the last couple weeks with the debacle...). As others have said, if you want a chance, go at a slow time. Midnight to 4am. If you want it to be in the day, then about 10-11am on a weekday.
Not O'hare but I know a gentleman that flew a 182 into Atlanta Hartsfield a few years ago to pick up his daughter.
On the way in they put him in an infinite hold. When he did get sequenced the jet traffic was eating his lunch and the tower was constantly giving him the old "keep speed as much as possible" routine.
Upon getting ready to leave his time on the ramp,taxiing and waiting was close to 45 minutes
He kinda got the feeling he was not welcome there
He says he would drive to Atlanta 5 times over rather than repeat that trip
I don't know why he had to get into Hartsfield instead of one of the feeder airports around there
If you do it, I'll give some actual advice. If ORD is landing to the west, You'll probably be expected to remain below the class B until you are approaching the shoreline so you aren't in the way of departures climbing off the airport. Call us from 20 or more miles out so we can figure out what to do with you. I would suggesting positioning yourself north of the airport prior to calling, otherwise you may get assigned the far south runway.
Once you're cleared into the B on a heading, you'll probably be expected to get some traffic in sight to follow, and you're going to be vectored pretty tight behind them with you providing your own visual and wake turbulence separation.
Listen carefully and make sure you are doing what the controller tells you, not what you think you should be doing. I worked a VFR C172 into ORD this summer that second-guessed every instruction I gave him and it really congested the frequency because he thought he had the big pictures (he didnt).
Why would you want to do that? There are far more friendly fields not far from ORD.
Kind of like flying into ATL, you'd be much better off landing at FTY or PDK, and getting some ground transportation. FTY is probably a quicker drive, but from PDK you can ride the train and it will drop you off in the terminal.
If you just want to get it in your logbook, go on a weekend at around midnight.
If you're going to visit the area, well, don't bother with ORD - Go to 06C instead (or another airport if it's closer on the ground). The money you save in fees will likely pay for your rental car.
I suggest 06C because it's much more 150-friendly, has no landing/ramp fees, and a regular-guy FBO (not $ignature etc). Most of the other airports in the immediate vicinity are towered, and I believe all of the towered airports in the Chicago area have hefty ramp fees.