We describe a new and computationally efficient technique for global three-dimensional modeling of stratospheric chemistry. This technique involves integrating a photochemical package along a large number of independent trajectories to produce a Lagrangian view of the atmosphere. Although Lagrangian chemical modeling with trajectories is an established procedure, this extension of integrating chemistry along a large number of domain-filling trajectories is a novel technique. This technique is complementary to three-dimensional Eulerian chemical transport modeling and avoids spurious mixing caused by low resolutions or diffusive transport schemes in these models. We illustrate the technique by studying the chlorine activation in the Arctic winter lower stratosphere. A photochemical model was integrated along large ensembles of calculated trajectories between 20 and 100 mbar for the 1991/1992 winter in order to produce a three-dimensional chemical picture. Large amounts of chlorine was activated at low altitudes (80 to 100 mbar) as well as altitudes near 50 mbar. This activated air was well contained at all levels, with little indication of mixing into lower latitudes. Model results for early January 1992 were compared to daily Microwave Limb Sounder (MLS) ClO observations at 465 K. The structure and evolution of the activated chlorine was well reproduced, giving faith in the technique, although absolute modeled ClO amounts were smaller than the MLS data. A larger number of domain-filling isentropic trajectories were also run at 475 K to produce a higher-resolution picture of vortex evolution in late January 1992. The model successfully reproduced the wave breaking events which characterized this period causing transport of activated air to lower latitudes.¿ 1997 American Geophysical Union