The surface tension of a freshly extruded pendant drop of a nanoemulsion, 4-cyano-4'-hexylbiphenyl or 6CB (a liquid crystal) in water, exhibits an unusual surface nucleation phenomenon. Initially the surface tension is that of pure water; however, after a surface nucleation time, the surface tension decreases suddenly in magnitude. This nucleation time, of hundreds to thousands of seconds, depends strongly upon (i) the 6CB concentration in water, (ii) the 6CB nanodroplet size, and (iii) the temperature. Similar behavior is observed in both the isotropic and nematic phases of 6CB; thus, this surface nucleation phenomenon is unrelated to this system's liquid crystalline properties. The observed surface nucleation behavior can be explained via considerations of the nanoemulsion's bulk entropy together with the number of 6CB nanodroplets in the vicinity of the surface.