Chicago features music by John Kander and lyrics by Fred Ebb
Chicago is a musical.
(See where this is going?)
Without its catchy songs and jazzy numbers, it would be pretty darn boring. Person commits a crime. Wants to be famous. Yawn. That's a story we've seen in the real world plenty of times. But the music takes it to another level. It furthers the plot and explains the characters in a way that gets them stuck in your head.
Making it a musical leaves us in the audience singing and dancing along—and making us complicit in Roxie's rise to infamy. You may think she's reprehensible for cashing in on a crime, but it wouldn't happen if the public didn't love it.
The music in the film is closer to the 1975 original production, as opposed to the popular 1996 revival starring Bebe Neuwirth as Velma, which featured a few songs not in the film. John Kander and Fred Ebb are also responsible for the music in Cabaret (1972). These guys know their jazz.