Abstract We study the optical response of eccentric nanoshells (i.e., spherical nanoparticles with an eccentric spherical inclusion) in the near and the far field through finite-difference time-domain simulations. Plasmon hybridization theory is used to explain the obtained results. The eccentricity generates a far-field optical spectrum with various plasmon peaks. The number, position, and width of the peaks depend on the core offset. Near-field enhancements in the surroundings of these structures are significantly larger than those obtained for equivalent concentric nanoshells and, more importantly, they are almost independent of the illumination conditions. This opens up the door for using eccentric nanoshells in applications requiring intense near-field enhancements.