It is almost impossible to discuss Chicago history without mentioning A.T. Andreas' 1884 History of Chicago. The Municipal Reference desk keeps the three large volumes of the 1975 reprint close at hand and constantly uses them to answer questions.
Andreas did not so much write history, as vacuum up information and print it. Thus, you can find maps and pictures of people, things, events and places. Almost every Chicago history writer since his day has shamelessly borrowed Andreas' illustrations.
He has lists and biographies of early voters, volunteer firemen, clergy, lawyers and every other category of people. Statistics and eyewitness accounts are other strengths. There are hundreds of pages of accounts of the Great Chicago Fire of 1871 and its origins.
Since most of Chicago's printed and manuscript material burned in the Great Fire, Andreas is often the only source of information about early Chicago. Where else could you find marriage statistics from the 1830s?
All of this information makes Andreas more of a reference and a (fun) browsing source rather than a fun read. However, we use it hundreds of times more often than scholarly histories such as Bessie Louise Pierce's History of Chicago.
The one volumeHistory of Cook County, Illinois (and reprint) focuses on the suburban area. However, at the time, Chicago's boundaries were roughly the Lake, 39th Street, Cicero and Fullerton. Thus, it too, is a history of Chicago.
Copies of both the original editions and the reprints are rare and expensive. There are print-on-demand publishers, but you should probably check the quality before buying. However, CPL's copies are available for reference at multiple locations.