Okay, there's not actually a Chicago Day, but on March 4, 1837, the City of Chicago charter was enacted into law by the state legislature (thereby incorproating Chicago as a city). Population: 4,170. You can learn more here and here.
For the record, my high school had a larger student body. (When I graduated in 1985, we had about 4500; at its largest, the school had a student body of around 9000).
Also of note, the new building, built in the 1930s, has one of the largest art collections of any high school in the nation.