I just started doing Crossfit this month at Atlas Crossfit (Erie/Orleans, www.atlascrossfit.com. If you work in the loop this could be a good option. I'm only a few weeks in and can't speak to how any other locations operate, but trust me they make SURE you know what you are doing before classes start. I am doing the "basic training" right now and they literally critique your form on push-ups and squats from the start before moving on to anything more complicated. We are in week three now and are now doing olympic lifts. Basic training is 4 weeks long, at which point you can "qualify" for Crossfit level 1. In other words, if you aren't an expert you are phased into it to ensure that you know what you are doing and don't hurt yourself.
The trainers there each seem to have their own specialties, so they change who is teaching specific basic training classes based on what we are learning that day and who is the expert in that area. The basic training classes are an hour long each, and about 45 minutes of that is focused solely on form and making sure we aren't (to speak to your concern) injuring ourselves.
As far as the previous comment that is tends to be a "bro" thing, I would strongly disagree. The clients in the normal classes tend to be about 80/20 male to female, about a third of the instructors I have seen appear to be female, and my class is 25% female and 50% over 40 years old. They scale everything based on ability and skill and work closely with anyone that is struggling. I really respect everyone that I have worked with so far there and have really enjoyed it.
Again, I can't speak to any other locations, but there does appear to be a crossfit gym on Milwaukee at 1064 N Milwaukee that might be a better option towards Bucktown, and another on Clybourn south of Armitage.