A thug breached security at a Times Square hotel, sneaked into a room and had a terrifying encounter with a maid, sources told The Post yesterday.

Cops said the incident occurred Tuesday at about 9:30 a.m. at the Marriott Marquis, cops said, when the man followed a maid into a room she was cleaning and hid in a closet.

When she opened the door, he jumped out, shoved her out of the way, and ran out of the hotel.

The suspect is still at large.