Chaotic transport in the Northern Hemisphere stratosphere is studied with an isentropic Lagrangian transport model. Ensemble statistics of trajectories are computed for 2-month periods in the winters of 1992 to 1997 by using United Kingdom Meteorological Office assimilated winds. In the midlatitudes, quasi-stationary anticyclones combine with the jet to produce flying and trapping events of particle trajectories. The flight time probability density functions (PDFs) are described by power laws with a decay exponent of less than 3, which indicates that the trajectories can be characterized as Lévy flights (random walk processes with divergent second moment). These flight and trapping events lead to superdiffusive zonal dispersion. The relationship between the power law decay exponents and the zonal mean and variance exponents is consistent with an analytical derivation. The scaled PDFs of zonal displacement converge to a self-similar limiting distribution, suggesting the existence of a scale-invariant regime. The skewness and kurtosis of the PDFs also converge to constant values after about 40 days, which supports the self-similarity behavior in Lagrangian trajectories.