The three-dimensional (3-D) formulation of the Chemical Lagrangian Model of the Stratosphere (CLaMS-3d) is presented that extends the isentropic version of CLaMS to cross-isentropic transport. The cross-isentropic velocities of the Lagrangian air parcels are calculated with a radiation module and by taking into account profiles of ozone and water vapor derived from a HALOE climatology. The 3-D extension of mixing maintains the most important feature of the 2-D version as mixing is mainly controlled by the horizontal deformations of the wind fields. In the 3-D version, mixing is additionally driven by the vertical shear in the flow. The impact of the intensity of mixing in the 3-D model formulation on simulated tracer distributions is elucidated by comparing observations of CH4, Halon-1211, and ozone from satellite, balloon, and ER-2 aircraft during the SOLVE/THESEO-2000 campaign. CLaMS-3d simulations span the time period from early December 1999 to the middle of March 2000, with air parcels extending over the Northern Hemisphere in the vertical range between 350 and 1400 K. The adjustment of the CLaMS-3d mixing parameters to optimize agreement with observations was obtained for strongly inhomogeneous, deformation-induced mixing that affects only about 10% of the air parcels per day. The optimal choice of the aspect ratio α defining the ratio of the mean horizontal and vertical separation between the air parcels was determined to be 250 for model configuration with a horizontal resolution r0 = 100 km. By transporting ozone in CLaMS-3d as a passive tracer, the chemical ozone loss was inferred as the difference between the observed and simulated ozone profiles. The results show, in agreement with previous studies, a substantial ozone loss between 380 and 520 K with a maximum loss at 460 K of about 1.9 ppmv, i.e., of over 60% locally, from December to the middle of March 2000. During this period, the impact of isentropic mixing across the vortex edge outweighs the effect of the spatially inhomogeneous (differential) descent on the tracer/ozone correlations in the vortex. Mixing into the vortex shifts the early winter reference tracer/ozone correlation to higher values, which may lead to an underestimate of chemical ozone loss, on average by 0.4 and 0.1 ppmv in the entire vortex and the vortex core, respectively.