:The borders appear to have been set at 12th Street and Halsted Street after the 1871 fire (see this article); I have to guess that city limits formed the other two boundaries but haven't found any information on that in the ten minutes I've been searching.

That same article indicates that the fire limits were expanded in 1874 (after a second major fire) to cover the whole city. That may contradict the Humboldt Park article, but I'm not sure.  In any case, the fire limits survive on as chapter 13-116 of the current Chicago Municipal Code: they cover "all zoning districts within the corporate limits classified B1-1 through B7-7 and C1-1 through C-4, as defined in the Comprehensive Zoning Ordinance of May 29, 1957, as amended, together with an additional 200 feet in all directions from the outer limits of each area or areas so classified." This appears to mean that most business and commercial districts in Chicago are governed by the fire limits regulations, but it's hard to tell. The 1957 zoning ordinance has been superseded and the City's online zoning map doesn't have the fire limits noted on it.