Illinois Naturalization Records at Ancestry
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.