What is the term length of a city mayor?

Until they die (or are voted out.) There are no term limits for the Mayor of Chicago. The first mayor Daley, Richard J. Daley served from 1955 until his death in December of 1976. His son Richard M. Daley has been mayor since 1989 and there is a very good possiblility that he will die in office, like his father, and he will definitely beat his father's record as the longest serving mayor of Chicago.