"Chicago" is written in free verse. It doesn't have a rhyme scheme or any sort of regular meter, and it's not written in a recognizable form (like a sonnet or villanelle).
Still, this doesn't mean that "Chicago" is a loosey-goosey formless mess. In fact, Sandburg lifts his form right from Walt Whitman, who is probably the most famous poet-chronicler of the American Experience.
Whitman was known for his long lines (like, really long lines), many of which began with the same words. (This is called anaphora). We see really long lines and plenty of anaphora in Sandburg's "Chicago":
And they tell me you are crooked and I answer: Yes, it is true I have seen the gunman kill and go free to kill again.
And they tell me you are brutal and my reply is: On the faces of women and children I have seen the marks of wanton hunger.
And having answered so I turn once more to those who sneer at this my city, and I give them back the sneer and say to them: (7-9)
And just like Whitman, Sandburg's long lines are often punctuated by short lines:
Building, breaking, rebuilding, (13-17)
So was Sandburg just ripping off Whitman's form? In the simplest terms: yes, yes he was. But borrowing Whitman's form was a way for Sandburg to both pay homage to the master and place himself in his poetic lineage. With "Chicago," Sandburg is putting his poems in dialogue with Whitman's. Check out Whitman's long poem "Song of Myself" here. See any cool connections with "Chicago"? We think you might find a lot.
And finally, let's stop for a sec to think about the meaning of all this good formal stuff. Sandburg's anaphora and long lines make us feel almost breathless. (Seriously, read the poem out loud and see if you can read one of the long lines in a single breath). Sandburg just has so much to say that he writes the poem in a kind of list format (which we see with both the anaphora and the short lines). It's like he has so much to say about good ol' Chicago, he has so much energy to capture in this poem, that he's just gotta list it all so that he doesn't forget anything!
Bareheaded? Check, Shoveling? Check. Wrecking? Check.
Check check check check check.