I’ve been working on my Cahill line for the last few days, mainly because I’m in the process of planning a research trip to Kane Co., Illinois to do some heavy-duty research on this line.
There are several indexes available for Kane Co. for naturalization records (both first and final papers) on microfilm through the FHL. I have been up and down them three times, and still cannot find anything on my 2nd great-grandfather, Thomas Cahill. Censuses indicate that he was naturalized by 1900 and with an immigration estimated in 1883/1884, this is certainly possible.
I did find a naturalization record  that I believe is for Thomas’ brother, John T (or F) Cahill. Unfortunately, there are only initials used on the form, the first of which could be read as a J, and I or, even a Q.
I retrieved this record from my FHL trip in October 2009 and filed it away as a possibility for John. After looking at the form more closely today, I’m pretty sure it’s for him. This is due in part to one of the witnesses, “Thos Cahill.”
Seeing as Thomas and John were brothers, who apparently immigrated about the same time, I’m assuming that the Thomas in this document is my 2nd great-grandfather, and “J T” is his brother John. The other witness, D F Garvey, is likely Denis Garvey who lived around the corner from John; John lived directly across the river from his brother in 1900. 
Although I still have not located papers for Thomas, this record does give me a clue, that coincides with Thomas’ 1900 census entry: Thomas was a citizen by April 1900, the session at which John filed his final papers. This record states: “…as well from the oath of the said J T Cahill as from the testimony of D. F Garvey and Thos Cahill who are known to be citizens of the United States…” (emphasis added).  So I know I am looking for naturalization records for Thomas before the April 1900 session of the Aurora City Court. Since Thomas apparently immigrated around 1883/1884, he could have filed the petition as early as 1885/1886, and final papers about 1888/1889. However, it is possible that he immigrated as a minor (under 21) and the rules may be slightly different.
John himself immigrated as a minor, as indicated in the naturalization record. According to other information about his birth, he was likely 17 when he came to America. The form itself is called “Final Certificate of Naturalization-Minor” and in the body of the form is reads: “…that the said applicant arrived in the United States a minor under the age of twenty-one years, and has resided within the limits and under the jurisdiction of the United States for and during the full term of five years last past, including three years previous to his arrival at the age of twenty-one years, and at least one year last past within the State of Illinois….” 
Family tradition holds that Thomas’s wife, Margaret Millett, had lived in Bristol, Kendall, Illinois before locating to Aurora. Kendall and Kane are neighboring counties, and Bristol is not at all far from Aurora. It is possible that Thomas lived there at some point as well, and naturalization records should be searched in Kendall County, since nothing so far has been found in Kane.
And with that, a new item goes on the never-ending research To Do List. Hopefully it will be a successful search!
1. Kane County, Illinois, Naturalization Records62: 534, J T Cahill; FHL microfilm 1,481,635.
2.1900 U.S. census population schedule, Aurora, Kane County, Illinois, enumeration district (ED) 65, sheet 1B, dwelling 16, family 21, John F Cahill; digital images, Ancestry (www.ancestry.com : accessed November 14, 2008); citing National Archives and Records Administration microfilm T623, roll 310. Also, 1900 U.S. census population schedule, Aurora, Kane County, Illinois, enumeration district (ED) 65, sheet 10B, dwelling 301, family 213, Denis Garvey; digital images, Ancestry (www.ancestry.com : accessed March 19, 2011); citing National Archives and Records Administration microfilm T623, roll 310.
3. Kane County, Illinois, Naturalization Records62: 534, J T Cahill.