Virus-like particles are biomimetic delivery vehicles that cloak nanoscale cores inside coatings of viral capsid proteins, offering the potential for protecting their contents and targeting them to particular tissues and cells. To date, encapsidation has been demonstrated only for a relatively limited variety of core materials, such as compressible polymers and facetted nanocrystals, over a narrow range of cores sizes and of pH and ionic strength. Here, we encapsidate spherical nanodroplets of incompressible oil stabilized by adsorbed anionic surfactant using cationic capsid protein purified from cowpea chlorotic mottle virus. By imaging with transmission electron microscopy we show that, as the droplets become larger than the wild-type RNA core, the protein is forced to self-assemble into spherical shells that are not perfect icosahedra having special triangulation numbers characteristic of the Caspar-Klug hierarchy. Consequently, the distribution of protein conformations on larger droplets is significantly different than in the wild-type shell.