WBEZ's Curious City blog re-posted an bit from 2016 identifying the geographic center of Chicago:
Calculating a center point is straightforward for geographers now, according to Todd Schuble, manager of GIS Research for the University of Chicago’s Division of Social Sciences.
Modern mapping software can find the center of any boundary automatically, even one as oddly shaped as Chicago. The process involves looking for any spot that a boundary bends, noting the coordinates, and then averaging them.
So where does Schuble put Chicago’s exact geographic center?
“It’s approximately 31st and Western,” Schuble says. “The [Sanitary and Ship] canal runs right there. The geographic center point itself runs through the canal.”
Chicago does have a monument that marks the center of the city, it’s just that it’s not at the actual center point (which, again, sits in the canal, south of 31st and Western). This is where the politics come in.
In 1979 outgoing Chicago Mayor Michael Bilandic presided over a ceremony declaring the intersection of W. 37th and S. Honore streets in the McKinley Park neighborhood the city’s geographic center point. There was even a white sign with black letters reading “Welcome to W 37th and S Honore Streets, The Geographic Center of Chicago, Greatest City in America.”
Mayor Bilandic was not the intellectual giant among our historical mayors. He lost the 1979 election by declaring, in the worst winter in recorded history, "snow melts." And so, apparently, he also got the geography of the city wrong, forgetting that we'd annexed the land that is now O'Hare in 1959.
The monument is still there; just check Google Street View.