We have used a three-dimensional (3D) chemical transport model (CTM) to investigate the variation in Arctic winter-spring chemical ozone loss from 1991--2003, and its observed correlation with low temperatures. The CTM (SLIMCAT) has been updated based on recent field and laboratory results and contains improved treatments of transport, chemistry and denitrification. In contrast to previous model studies, the CTM now gives a good simulation of the observed O3 loss throughout the years studied. The model reproduces the large column loss of cold winters and also captures the shape of the ozone loss profile. The variation of O3 loss with interannual variations in temperature is also well reproduced. Hence we show that for the first time a 3D stratospheric model is able to reproduce the past climate sensitivity of Arctic ozone depletion on temperature. This new capability is an essential prerequisite for model predictions of the future of the Arctic ozone layer in a changing climate. With realistic transport, chemistry-climate models with similar chemical modules should be able to reproduce polar chemical ozone depletion over the range of temperatures experienced so far.