The Chicago Public Library offers the following explanation of the flag's symbolism, which was originally designed (two stars) by lawyer turned writer, reporter and drama critic, Wallace Rice (1859-1939), and adopted in 1917:
The Municipal Flag of Chicago consists of three White stripes separated by two stripes of Blue with four Red six-pointed stars on the center stripe of White.
The White Stripes:
Top White Stripe represents the North side of the city.
Center White Stripe represents the West side of the city.
Bottom White Stripe represents the South side of the city.
The Blue Stripes:
Top Blue Stripe represents Lake Michigan and the North Branch of the Chicago River.
Bottom Blue Stripe represents the South Branch of the Chicago River and the Great Canal.
The Red Stars:
The First Red Star represents Fort Dearborn (added by City Council in 1939).
The Points of the First Red Star Signify:
The Second Red Star represents the Chicago Fire of October 8-10, 1871.
The Points of the Second Red Star Signify:
Esthetics [original spelling by Rice)
The Third Red Star represents the World's Columbian Exposition of 1893.
The Points of the Third Red Star Signify History of the Area:
Great Britain 1763
Northwest Territory 1798
Indian Territory 1802
Illinois Statehood 1818
The Fourth Red Star represents the Century of Progress Exposition of 1933 (added by City Council in 1933)
The Points of the Fourth Red Star Signify:
World's Third Largest City
City's Latin Motto
“I will” Motto
Great Central Market
For more information on the Flag of Chicago, see T. E. Whalen's impressive bibliography, beginning with the 1892 "Tribune" offer of $100 for the best suggestions of "municipal colors": The Municipal Flag of Chicago
Also recommended:Flags of the World and MUNICIPAL FLAG OF THE CITY OF CHICAGO from the Eastland Memorial Society.
Sidebar: Wallace Rice, a prolific writer with eclectic interests, was a member of the Illinois State Historical Society,the Chicago Historical Society, the Cliffdwellers, the Society of Midland Authors, the Stage Guild, and the Playwrights Theater. For examples of his writing, see Internet Archive.
My thanks to Gregory Tejeda at Chicago Argus for posing the question on his blog.