The large amplitude oscillations of the shape of Neptune's Great Dark Spot are well reproduced by simple dynamical models of an isolated vortex embedded in a background shear flow. From the time series of the aspect ratio and inclination of the vortex values are estimated for the background shear and the mean vorticity of the Great Dark Spot, and a lower bound is placed on the value of the Rossby deformation radius. These models imply the existence of a planetary-scale zone of deterministic chaotic advection in the atmosphere of Neptune.