We have built a torsional pendulum based on an individual single-walled carbon nanotube, which is used as a torsional spring and mechanical support for the moving part. The moving part can be rotated by an electric field, resulting in large but fully elastic torsional deformations of the nanotube. As a result of the extremely small restoring force associated with the torsional deformation of a single molecule, unusually large oscillations are excited by the thermal energy of the pendulum. By diffraction analysis, we are able to determine the handedness of the molecule in our device. Mechanical devices with molecular-scale components are potential building blocks for nanoelectromechanical systems and may also serve as sensors or actuators.