Online Illinois Naturalization Indexes and Records
For Illinois there is a soundex index available on microfilm from the National Archives (Microfilm Publication M1285). It is also indexed online at Ancestry and FamilySearch...
Soundex Index to Naturalization Petitions for the United States District and Circuit Courts, Northern District of Illinois, and Immigration & Naturalization Service District 9, 1840-1950
It covers the following Illinois counties: Boone, Bureau, Carroll, Champaign, Cook, DeKalb, DuPage, Ford, Fulton, Grundy, Henderson, Henry, Iroquois, Jo Daviess, Kane, Kankakee, Kendall, Knox, Lake, LaSalle, Lee, Livingston, Marshall, McHenry, McLean, Mercer, Ogle, Peoria, Putnam, Rock Island, Stark, Stephenson, Tazewell, Vermilion, Warren, Whiteside, Will, Winnebago, and Woodford. The 1840-1950 time frame varies by county.
Naturalization records for Cook County begin in 1871. The Cook County Naturalization records prior to that were destroyed in the Chicago fire.
This microfilm publication is also available at the LDS Family History Library in Salt Lake City so you can order the rolls from many local Family History Centers. Click on the title above for more information and a link to the microfilm roll numbers.
Chicago Voter Registration Records
Using these databases requires a subscription to Ancestry's U.S. genealogy records collection. These Chicago Voter Registrations are helpful because they give the year and place of Naturalization (one of four Cook County Courts) for many of the foreign born voters (who had become citizens). They also give country (or state) of birth and the address of the voter. The time frame is significant as the 1890 census was destroyed in a fire.