Most high schools probably wouldn't want to tackle Chicago. It's a big ask. However, it's not impossible. I work at a Catholic college and we did it two years ago, and we did a great job of it (yah boo sucks to you, PeggySeldon et al).
It takes a very experienced director and a special group of kids to do the show. The director and I discussed the wisdom of doing it (I'm the musical director) and decided we were up to it. The cast need to understand the basis of the show's satire and be mature enough to cope with the sexual innuendo, smoking, drinking and all the other facets of the underworld portrayed in the show.
It also requires a lot from the school leadership. Our principal greatly trusted our director and our director made it plain to the audience in a variety of ways that our production was critiquing the sexy, sordid, exploitative aspects of the show, rather than glamourising them. It is, after all, a satire and not a documentary.
One of the ways we achieved this was to use a video screen in the set. Over the final dance number with Velma and Roxie, we flashed images of current "celebrities" (media whores and parasites) like Paris Hilton and Lindsay Lohan, helping the audience to understand the message of the show and the ideas being satirised.
So - yeah, it's tricky, but if your school has the appropriate climate and culture and your cast is good enough to rise to the challenge, then go for it.