A stable nanoemulsion consisting of nanometer-sized oil droplets in water having a self-standing capability was prepared by high-pressure emulsification. The nanoemulsion does not flow and has a yield stress. This nonfluidity is ascribed to the crystal-like lattice structure of nanodroplets. The lattice structure was observed by transmission electron microscopy of a freeze-fractured surface of the specimen. Small-angle neutron scattering (SANS) revealed the presence of all ordered structure in addition to spherical domains with a radius of 17 nm. This long-range order is, in principle, due to electrostatic repulsive interaction between charged nanodroplets. Dynamic light scattering (DLS) showed two relaxation modes, one for the collective motion of the lattice and the other for the translational diffusion of the nanodroplets. Dilution of the nanoemulsion resulted in a transition from a crystal-like structure to a typical colloidal solution.