CHICAGO — Two African-American women are headed for a runoff in the Chicago mayor’s race, setting up an election that will make history.

Lori Lightfoot, a former federal prosecutor and sharp critic of the status quo at City Hall, and Toni Preckwinkle, the county board president and chairwoman of the county’s Democratic Party, will face one another in a runoff election set for April, according to The Associated Press.

The third top vote-getter — William M. Daley, a member of Chicago’s political dynasty of Daleys — earlier conceded defeat.

Either Ms. Lightfoot or Ms. Preckwinkle would be the first African-American woman to lead the nation’s third largest city, succeeding Mayor Rahm Emanuel as mayor. Only one other woman, Jane Byrne, has been elected mayor, in 1979. If Ms. Lightfoot were to win, she also would be the first openly gay mayor of Chicago.