A monodisperse emulsion of oil droplets in water (hydrocarbon radius approximately 8 nm) stabilized by the nonionic surfactant pentaoxyethylene glycol dodecyl ether (C(12)E(5)) is prepared from a stable microemulsion containing the oil droplets by lowering the temperature across a phase boundary. At equilibrium a droplet emulsion phase exists in conjunction with excess oil. The first stage in the equilibration process is followed by measuring the turbidity. It is observed that for small temperature quenches the system is metastable, showing no measurable changes over at least 1 h. There is a sharp boundary between metastable and unstable regions, and this, like the phase boundary, is virtually independent of droplet concentration in the range 5-20%. The observation is interpreted qualitatively as an Ostwald ripening-like process, where a few oil droplets grow, allowing the majority to shrink in size. The presence of a nucleation threshold can be understood in terms of the curvature free energy of the surfactant film.