One of Cathie Black’s thorniest first assignments as schools chancellor is what to do about the 1,200 “excess” teachers who still don’t have regular jobs but get full pay and benefits, officials said yesterday.

A decision on whether to assign these teachers-in-limbo to schools or yank them from the payroll is a “top priority” for Black and the teachers union.

Of the 1,232 teachers who lost jobs when schools were phased out or downsized since 2006, nearly half have been without new jobs for up to three years, the Department of Education said yesterday.

More than 100 remain unplaced for four years. Sixty percent of them have not even applied for a new job or attended a job fair, the DOE said. The Absent Teacher Reserve pool costs more than $100 million a year, the DOE said.

Teachers union President Michael Mulgrew blamed the DOE, saying it “refuses to permanently place” the teachers in schools. Mulgrew said the “ATR” teachers save the DOE “an estimated $50 million a year” by substituting for regular teachers out sick or on leave, but he added, “It’s not the best use of these teachers’ talents.”

A November 2008 agreement to give principals extra money as incentives to hire the excess teachers expired Tuesday.

Meanwhile, a Brooklyn parent and lawyer filed a suit challenging the waiver that Black was granted allowing her to be chancellor.

Eric Snyder argued that Black, who needed the waiver because she is not a professional educator, did not have the appropriate degree for the position.