LONG-TERM depletion of ozone has been observed since the early 1980s in the Antarctic polar vortex, and more recently at midlatitudes in both hemispheres, with most of the ozone loss occurring in the lower stratosphere(1). Insufficient measurements of ozone exist, however, to determine decadal trends in ozone concentration in the Arctic winter. Several studies of ozone concentrations in the Arctic vortex have inferred that chemical ozone loss has occurred(2-11); but because natural variations in ozone concentration at any given location can be large, deducing long-term trends from time series is fraught with difficulties. The approaches used previously have often been indirect, typically relying on relationships between ozone and long-lived tracers. Most recently Manney et al.(11) used such an approach, based on satellite measurements, to conclude that the observed ozone decrease of about 20% in the lower stratosphere in February and March 1993 was caused by chemical, rather than dynamical, processes. Here we report the results of a new approach to calculate chemical ozone destruction rates that allows us to compare ozone concentrations in specific air parcels at different times, thus avoiding the need to make assumptions about ozone/tracer ratios. For the Arctic vortex of the 1991-92 winter we find that, at 20 km altitude, chemical ozone loss occurred only between early January and mid February and that the loss is proportional to the exposure to sunlight. The timing and magnitude are broadly consistent with existing understanding of photochemical ozone-depletion processes.