The optical properties of metals arise both from optical excitation of interband transitions and their collective electronic, or plasmon, response. Here, we examine the optical properties of Cu, whose strong interband transitions dominate its optical response in the visible region of the spectrum, in a nanoshell geometry. This nanostructure permits the geometrical tuning of the nanoparticle plasmon energy relative to the onset of interband transitions in the metal. Spectral overlap of the interband transitions of Cu with the nanoshell plasmon resonance results in a striking double-peaked plasmon resonance, a unique phenomenon previously unobserved in other noble or coinage metal nanostructures.