The poll of 600 randomly selected registered voters was taken for the Chicago Sun-Times on Wednesday, the day after Daley announced that he won't seek a seventh term in office.
The poll found 12 percent of those surveyed would vote for Cook County Sheriff Tom Dart, while 10 percent favored state Sen. James Meeks. They were the only candidates to score in double-digits.
Congressman Luis Gutierrez had the support of 9 percent of those polled, while Congressman Jesse Jackson Jr. had 8 percent and White House Chief of Staff Rahm Emanuel had 7 percent. Several other candidates split the remaining percentage.
The poll had an error margin of 4.3 percentage points.