Hypothetical Question: Can an airplane takeoff if it is sitting on a treadmill?

An airplane is sitting on a treadmill. Let's just say that the treadmill is a mile long to give plenty of takeoff room. The treadmill does not have a motor. Let's also suppose that the treadmill rolls very easily and that the airplane does not have the brakes on. Normal gravity, airflow, friction, and such apply. Can this imaginary airplane take off?