This underground jazz club had the perfect speakeasy feel to it and offered some of the best live jazz I have heard, and I am from Chicago! The jazz alone was worth the visit! They had classic jazz, french jazz, and big band jazz performances.
It also has a great menu of food, though not in English so bring a translator, and has a large selection of fun signature drinks.
The only con: it is a very cramped and small venue, so get there early to get a good seat.