Illinois State Death Certificates
Copies of the death certificates from 1916-1947 can be ordered via interlibrary loan from the Family History Library or directly through a genealogist who lives in Springfield near the Illinois State Archives. I have used Molly's services in the past and have been pleased. She can only obtain those records between 1916 and 1947. Records after that date can be ordered from the county or the state. Usually it is cheaper to order genealogical copies from the county.
State registration of deaths began in Illinois in 1916 and records from that time on have been recorded at the state and county level. Records before that date were only recorded at the county level and may begin as early as 1877. Some of these pre-1916 death records have been microfilmed and may be located at a branch of the Illinois Regional Archives or via interlibrary loan through your local Family History Library. If they were originally recorded at the county level, the county will have the original. It is usually cheaper to order from the Illinois Regional Archives or to borrow the film from the Family History Library. The Illinois State Archives also has a partial index of pre-1916 death certificates on their website as well.
For Cook County death certificates pre-1916, I have used the services of at Cynthia at http://www.chicagogenealogy.com/. Molly at http://www.mollx.com/ also can access some pre-1916 certificates in Illinois outside the Cook County area.