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Using the finite-difference time-domain method, we investigate the plasmonic mode spectrum of a metallic nanostructure consisting of a concentric arrangement of a solid disk and a surrounding ring. We demonstrate that the energies of the plasmon modes depend sensitively on the structural parameters of the disk and the ring. We show that the nature of the plasmon modes can be understood simply as a hybridization of individual disk and ring plasmons. This interaction results in a redshifted bonding plasmon resonance of significantly narrower linewidth and larger electromagnetic field enhancements than the parent plasmons. This highly tunable nanostructure has significant potential as a substrate for surface enhanced spectroscopies.