Finding the lowest energy configuration of N unit charges on a sphere, known as Thomson's problem, is a long-standing query which has only been studied via numerical simulations. We present its physical realization using multiply charged He nanodroplets. The charge positions are determined by x-ray coherent diffractive imaging with Xe as a contrast agent. In neutral droplets, filaments resulting from Xe atoms condensing on quantum vortices are observed. Unique to charged droplets, however, Xe clusters that condense on charges are distributed on the surface in lattice-like structures, introducing He droplets as experimental model systems for the study of Thomson's problem.
