We develop a theory of near-field Raman enhancement in one-dimensional systems, and report supporting experimental results for carbon nanotubes. The enhancement is established by a laser-irradiated nanoplasmonic structure acting as an optical antenna. The near-field Raman intensity is inversely proportional to the 10th power of the separation between the enhancing structure and the one-dimensional system. Experimental data obtained from single-wall carbon nanotubes indicate that the Raman enhancement process is not significantly influenced by the specific phonon eigenvector, and is mainly defined by the properties of the nanoplasmonic structure.