The Regenstein’s “Map Collection”:http://www.lib.uchicago.edu/e/su/maps, among a goodly number of assorted (mostly sociological) maps of Chicago from 1890-1935 and 1990-2000, has a population density map of Chicago, circa 1930 online. It appears to be based on section (mile grid), rather than community area. Four major sectors of the city had more than 50,000 persons per square mile, even before “high-rises”:http://www.lib.uchicago.edu/e/su/maps/chisoc/G4104-C6-1933-U5-o.html sprouted outside downtown: the north lakefront (east of Halsted/Clark to Lawrence); west and east Ukrainian Village/Wicker Park, from Humboldt Park to the river; Pilsen and Lawndale; and the Black Belt, Washington Park, and Woodlawn. Now, perhaps two CAs would come close; most of the above areas now average 20-30,000 per square mile, with the abandoned South Side much lower.
Recovering this density should be Chicago’s goal. But let’s keep in mind that much of this density probably derived from living conditions that we would today consider cramped, crowded, and unsanitary.