Carbon nanotubes are promising building blocks for various nanoelectronic components. A highly desirable geometry for such applications is a coil. However, coiled nanotube structures reported so far were inherently defective or had no free ends accessible for contacting. Here we demonstrate the spontaneous self-coiling of single-wall carbon nanotubes into defect-free coils of up to more than 70 turns with identical diameter and chirality, and free ends. We characterize the structure, formation mechanism, and electrical properties of these coils by different microscopies, molecular dynamics simulations, Raman spectroscopy, and electrical and magnetic measurements. The coils are highly conductive, as expected for defect-free carbon nanotubes, but adjacent nanotube segments in the coil are more highly coupled than in regular bundles of single-wall carbon nanotubes, owing to their perfect crystal momentum matching, which enables tunneling between the turns. Although this behavior does not yet enable the performance of these nanotube coils as inductive devices, it does point a clear path for their realization. Hence, this study represents a major step toward the production of many different nanotube coil devices, including inductors, electromagnets, transformers, and dynamos.