The bank, which is located off Airport Road on 101 Banks Drive near Interstate 40, was robbed at 12:52 p.m., reports state.
Chapel Hill Police Chief Gregg Jarvies said the Wachovia Bank is not believed to have had problems with robberies in the past.
The man, photographed by a surveillance camera, left the scene with an undetermined amount of cash, reports state.
The man entered the bank through the east entrance and handed a note demanding money to the teller, reports state.
Chapel Hill police are not releasing the contents of the note.
Police also are not ruling out the possibility that the man was armed.
"There was mention of his having a weapon," Jarvies said.
But it could not be confirmed that a weapon was present during the robbery, Jarvies said.
"No weapon was seen," he said.