A police report says the man destroyed a burglar alarm and "consumed the food." He was still sitting on a stool when the general manager arrived at 6:10 a.m., police said. The incident occurred on New Year's Day.
Authorities said the man fled into a nearby McDonald's restaurant and then disappeared. In a picture distributed by the police, the man is wearing a floppy hat, baggy pants and a backpack.
Employees of the Chipotle, at Sixth and F streets NW, declined to comment on Tuesday. The police report lists the food as a "tray of barbacoa," a Mexican beef barbecue.
Correction: In an earlier version of this article, the headline and first paragraph incorrectly said the man who broke into the restaurant ate pulled pork.