The poem begins when the speaker addresses the city of Chicago with five short lines. He calls Chicago a series of names—it's a "Hog Butcher" and a "Tool Maker" and a "Stacker of Wheat" (and a bunch of other things too). The Chicago that the speaker personifies is burly and tough.
Then, in longer lines, the speaker describes the life of the city. A mysterious "they" tells the speaker that Chicago is "wicked," "crooked," and "brutal," and the speaker agrees with all of these judgments. He has seen prostitutes, killers, and starving families. But the speaker responds to this "they" and pronounces Chicago is "so proud to be alive and coarse and strong and cunning." It's a vibrant and dynamic city, and the speaker finds beauty in it, despite its dark corners.
The speaker then describes Chicago again in a series of short lines. Chicago is constantly "building, breaking, rebuilding." This is the life cycle of the city.
Then the speaker describes Chicago even further. The city almost becomes the very people who inhabit it (freaky, right?). The city feels the pulse and the "the heart of the people."
In the last line of "Chicago," the speaker repeats the first few phrases of the poem. He once again calls Chicago "Hog Butcher" and "Tool Maker," and he says that the city is proud to have these names. Chicago, you rock, the poem says.