Scanning tunneling microscopy (STM) images of carbon nanotubes grown by the catalytic cracking of hydrocarbons, which exhibit a well-defined axial periodicity in the 1 nm range, are reported. The data are interpreted as tightly wound, single-wall, coiled carbon nanotubes with an interspire distance of 0.34 nm as the distance between graphene layers in graphite or the distance of single-wall carbon nanotubes in ropes.