Using electrodynamics calculations, we have discovered one dimensional array structures built from spherical silver nanoparticles that produce remarkably narrow (similar to meV or less) plasmon resonance spectra upon irradiation with light that is polarized perpendicular to the array axis. The narrow lines require a minimum particle radius of about 30 nm to achieve. Variations of the plasmon resonance wavelength, extinction efficiency and width with particle size, array structure, interparticle distance and polarization direction are examined, and conditions which lead to the smallest widths are demonstrated. A simple analytical expression valid for infinite lattices shows that the sharp resonance arises from cancellation between the single particle width and the imaginary part of the radiative dipolar interaction. (C) 2004 American Institute of Physics.