there's rhythm night club : http://www.drumallnight.com/
which has a lot of drum performances.
There's also a lot of african drumming troups locally which teach classes and occasionally have performances, they also sometimes bring over musicians to perform, for example last year we saw a djembe performance in a church in Hyde Park by a couple djembe folks who had worked with les ballets africaines.
I know the drumming classes at Old Town put on performances as part of their student recitals, they also feature professional performances sometimes as part of their afrofolk worldwide series (which are also free) there was one this past weekend at the South Shore cultural center - the link for the afrofolk series is http://www.oldtownschool.org/afrofolk/
Another good source for these performances is the afropop - http://www.afropop.org/
site, which has a link for upcoming performances in chicago, you can also sign up for an email newsletter and get them in your inbox