"What do you do with a 15-year-old who is a transvestite?"

New York City Schools Chancellor Nathan Quinones posed that question today as he defended the city's decision to fund an instructional program for 20 homosexual teen-agers at a Greenwich Village church.

The $50,000 program, which began in April, was informally named the Harvey Milk School by its students in memory of the homosexual San Francisco supervisor who was murdered in 1978. But the "off-site unit," one of more than 35 programs that operate in prisons, drug-rehabilitation clinics and community groups, is not an accredited public school, Quinones said.

Quinones called a news conference after a front-page article in The New York Times called the program "a New York City public school" and quoted its organizers as saying it was "the first public school in the United States to be geared specifically to homosexual adolescents."

At the gracious stone Washington Square Church this morning, four teen-agers shielded their faces from television cameras as they entered the church building that houses their classroom. Three Board of Education security guards kept reporters at a distance.

Steve Ashkinazy, clinical director of the Institute for the Protection of Lesbian and Gay Youth, said his nonprofit counseling group asked the city to join in sponsoring the program last November. In January, officials from the school system's division of off-site educational services agreed to provide one teacher and curriculum materials.

Ashkinazy said the program is expected to triple in size by the fall.

Students come from all parts of the city and receive credit toward a high school diploma at their regular schools. The institute, which also provides counseling for the 20 students, pays the church $500 rent a month for the classroom.

Comparing the Harvey Milk School to programs for pregnant teen-agers, prison inmates and drug addicts, Quinones said the homosexual students "have been abused in many cases by their families and by their peers at school. These are dropouts. They are not just homosexuals. They engage in flamboyant behavior . . . . If it weren't for this program, they would be cruising on the West Side of Manhattan to get some money or some attention."

Students in the program have been "harassed, beaten up or labeled as problems and kicked out" of city schools, Ashkinazy said. Some will return to the regular school system.

The students refused to talk to reporters, Ashkinazy said, "because they are shaken up over the publicity. Every time gay and lesbian people try to do something ordinary, it gets a lot of attention. But nobody minds the fact that there are hundreds of gay and lesbian teen-agers on the Greenwich Village waterfront who are getting involved in drugs and prostitution and being coerced into pornography rings."

Ashkinazy said the students in the program follow a regular high school curriculum. "But when they're asked to do book reviews, they can choose books with gay characters. They're learning 'Hamlet' now, and most Shakespearean scholars agree that he was a homosexual. The kids discuss that."

Jeff Leavy, executive director of the National Gay Task Force, said he knows of no similar program elsewhere. District of Columbia schools have no such program.

"While adults and students certainly have a right to choose their personal life styles, life styles are not a determinant of appropriate educational programs," D.C. School Superintendent Floretta McKenzie said in a statement.