We propose a new drive mechanism for carbon nanotube (CNT) motors, based upon the torque generated by a flux of electrons passing through a chiral nanotube. The structure of interest comprises a double-walled CNT formed from, for example, an achiral outer tube encompassing a chiral inner tube. Through a detailed analysis of electrons passing through such a "windmill," we find that the current, due to a potential difference applied to the outer CNT, generates sufficient torque to overcome the static and dynamic frictional forces that exist between the inner and outer walls, thereby causing the inner tube to rotate.