The Lagrangian evolution of material lines within the northern hemisphere winter stratospheric vortex is determined using isentropic winds and diabatic heating rates obtained from the NASA Langley Research Center (LaRC) atmospheric circulation model. Transient, subtropical anticyclones lead to deformation of the material lines near the edge of the polar vortex which then rapidly evolve into elongated filaments as material is drawn around the anticyclones. The rate of stretching of the material lines is shown to be exponential, with typical e-folding times of the order of 4 to 8 days. These results provide evidence for ''chaotic advection'' near the edge of the stratospheric polar vortex which leads to rapid mixing of vortex air tropical and midlatitude air. The characteristic timescales of these mixing processes and the extent to which the mixing penetrates the polar vortex have important implications for the dispersal of chemically perturbed air from the polar vortex throughout the northern hemisphere and attendent ozone depletion. ¿ American Geophysical Union 1993