Some binary mixtures exist as a single phase at high temperatures and as two phases at lower temperatures; rapid cooling therefore induces phase separation that proceeds through the initial formation of small particles and subsequent growth and coarsening. In solid and liquid media, this process leads to growing particles with a range of sizes, which eventually separate to form a macroscopically distinct phase. Such behaviour is of particular interest in systems composed of an isotropic fluid and a liquid crystal, where the random distribution of liquid-crystal droplets in an isotropic polymer matrix may give rise to interesting electro-optical properties. Here we report that a binary mixture consisting of an isotropic fluid and a liquid crystal forming the continuous phase does not fully separate into two phases, but self-organizes into highly ordered arrays of monodisperse colloidal droplet chains. We find that the size and spatial organization of the droplets are controlled by the orientational elasticity of the liquid-crystal phase and the defects caused by droplets exceeding a critical size. We expect that our approach to forming monodisperse, spatially ordered droplets in liquid crystals will allow the controlled design of ordered composites that may have useful rheological and optical properties.