A teenager was shot and killed outside a Queens public housing development early Sunday.

The 18-year-old victim was shot in the chest and back outside NYCHA’s Woodside Houses on 49th St. near 31st Ave. about 12:15 a.m., cops said.

Medics rushed him to Elmhurst Hospital but he could not be saved. His name was not immediately released.

His killer has not been caught.