Before 1916
Some counties in Illinois began keeping death records in 1877. An index to some of these records are available online in the Illinois Statewide Death Index, Pre-1916, a listing of the counties included and the date ranges can be found here. These records are housed within the county where the death occurred; a copy of of the record can be obtained from the county in which the death occurred. Many counties offer a genealogical copy, which is less expensive than a certified copy.
Index of Deaths 1916-1947 & 1916-1950
There are two different indexes of death records for time periods after 1916. Family Search hosts the Illinois Deaths and Stillbirths, 1916-1947. The Illinois state archives hosts the index, Illinois Death Certificates, 1916-1950.
Records after 1916
The state of Illinois offers a genealogical version of death records that are less expensive than certified copies of the record. Currently, a genealogical version is $10, while a certified copy is $19. Counties can also be contacted for the certificate and may be less expensive than contacting the state, for example, Dupage county only charges $5.