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We have assembled a three-dimensional (3D) plasmon ruler using an atomic force microscope (AFM) tip to manipulate single gold nanocrystals on top of electron beam lithography fabricated base layers. The 3D structures exhibit several polarization-dependent surface plasmon scattering peaks, including symmetric and asymmetric Fano resonances. We map these resonances as a function of the degree of asymmetry of the structure. We show that the coupled surface plasmon resonances are extremely sensitive to the position of the upper particle and that the resonances can be engineered and tuned using an AFM tip to move the upper nanocrystal just a few Angstroms.