A simple technique is described here that produces aligned arrays of carbon nanotubes. The alignment method is based on cutting thin slices (50 to 200 nanometers) of a nanotube-polymer composite. With this parallel and well-separated configuration of nanotubes it should be possible to measure individual tube properties and to demonstrate applications. The results demonstrate the nature of rheology, on nanometer scales, in composite media and flow-induced anisotropy produced by the cutting process. The fact that nanotubes do not break and are straightened after the cutting process also suggests that they have excellent mechanical properties.