Law enforcement officers said they responded to the business at 19300 Katy Freeway near Fry Road at about 9 a.m. on Friday.
Sheriff Ed Gonzalez said a man was on the restaurant's roof and refused to come down. In an afternoon update, Gonzalez said the man climbed to a lower level, where deputies took him into custody.
At one point, the sheriff said the Chick-fil-A was evacuated as a result. It's unclear how the man climbed onto the roof, but an investigation is ongoing.
According to the sheriff, the man is believed to have an open felony warrant from another county.