On November 4, Republican Judy Baar Topinka was re-elected to another four-year term as Comptroller of Illinois. But she died on December 10, before inauguration day for the newly-elected statewide executive officers. The Illinois Constitution says when one of those officers dies, the Governor may replace the officer; there is no provision for a special election.
There are technically two vacancies to fill: one for the remainder of the current term, which expires in a few weeks; and one for the next four year period. This article discusses the unresolved legal questions.
Topinka, 70, suffered a stroke on December 9. She was one of the most popular politicians in Illinois; see this story about her.