I would like to caution you right at onset that this movie is a BROADWAY MUSICAL brought to screen and that does not mean a movie with songs a la The Sound of Music. One of my friends had this impression and he has cussed me big time for recommending it as it did not fit into anything he has seen before :) I tend to agree that this form of entertainment (broadway musicals) is bit difficult to digest for the uninitiated.
Last Years Moulin Rouge was a real, thoroughly overproduced musical with complete accent on razzle-dazzle and showmanship. Bits and pieces of story was to weave the songs together. Chicago differs from it because it uses the songs to forward the story, not the other way round.
The plot is essentially a prison+courtroom drama. And you may expect this genre to succeed by crisp dialogues, brilliant arguments, solid performances etc. (remember Grisham movies/The Practice) Chicago dispenses all that with all that jazz ! It effectively uses musical interludes to give you the SAME rush of the courtroom dramas. Where it succeeds is in blending the musical format with a compelling true story not tailored for a musical.
In my opinion, a better example of this is the musical O Brother! released two years ago melding Homers Odyssey into a musical.
Movie uses metaphors in a very interesting way. Be it the way playing media like a puppet shows every artist tied to the strings, a puppet dance. Or Tap dancing scene that demonstrates Bills playing to the gallery/jury or the intro song for every character. It has this common thread. And this is what makes the movie watchable to a common movie-goer with no particular musical bent. Thats why, dont be shy, give it a try .. (Did you tap your legs to this ? then u do have the bent ;)
In bollywood movies, songs are your sutta/toilet breaks. Here I advise you to venture out only when the music stops playing, lest you miss out on that you came to see !
Thats all I can say, and thats all I understand about musicals anyway :)