Coiled carbon nanotubes were produced catalytically by thermal decomposition of hydrocarbon gas. After deposition on a silicon substrate, the three-dimensional structure of the helix-shaped multiwalled nanotubes can be visualized with atomic force microscopy. Helical structures of both chiralities are present in the nanotube deposits. For larger coil diameters (> 170 nm), force modulation microscopy allows one to probe the local elasticity along the length of the coil. Our results agree with the classical theory of elasticity. Similar to the case of straight nanotubes, the Young modulus of coiled multiwalled nanotubes remains comparable to the very high Young modulus of hexagonal graphene sheets.