The industrial prilling process provides a quick and reliable method for producing small pellets. These pellets are usually solidified droplets formed by the break-up of rotating liquid jets, which are typically non-Newtonian. An understanding of the factors that control the size of these droplets is important in delivering high-quality monodisperse pellets and also eliminating waste. In this paper, we investigate the instability of a rotating non-Newtonian liquid jet and in particular, we examine the case where the jet has an initial layer of surfactant along its interface. We use an asymptotic method to reduce the governing equations into a set of 1D equations and we solve these equations using a second-order finite difference scheme in order to investigate break-up and droplet formation. The size of parasitic satellite droplets, which can lead to greater inefficiencies, are investigated for a number of different parameter values.