Just 26 percent said she does and 23 percent were undecided. The poll has a margin of error of plus or minus 2.7 percentage points.
Black is the chairwoman of Hearst Magazines. Because she has no educational credentials, she would need a waiver from the state Education Department to serve as chancellor.
An eight-member advisory panel will weigh her qualifications at a meeting Tuesday in Manhattan.
Meantime, the poll found that Bloomberg is unhurt - and unhelped - by the recent announcement of a city budget with some service cuts, with a 57 - 33 percent overall approval rating and a negative 45 - 47 percent approval for his handling of the city budget.