A number of studies have demonstrated the importance of ozone in climate change simulations, for example concerning global warming projections and atmospheric dynamics. However, fully interactive atmospheric chemistry schemes needed for calculating changes in ozone are computationally expensive. Climate modelers therefore often use climatological ozone fields, which are typically neither consistent with the actual climate state simulated by each model nor with the specific climate change scenario. This limitation applies in particular to standard modeling experiments such as preindustrial control or abrupt 4xCO2 climate sensitivity simulations. Here we suggest a novel method using a simple linear machine learning regression algorithm to predict ozone distributions for preindustrial and abrupt 4xCO2 simulations. Using the atmospheric temperature field as the only input, the regression reliably predicts three-dimensional ozone distributions at monthly to daily time intervals. In particular, the representation of stratospheric ozone variability is much improved compared with a fixed climatology, which is important for interactions with dynamical phenomena such as the polar vortices and the Quasi-Biennial Oscillation. Our method requires training data covering only a fraction of the usual length of simulations and thus promises to be an important stepping stone towards a range of new computationally efficient methods to consider ozone changes in long climate simulations. We highlight key development steps to further improve and extend the scope of machine learning-based ozone parameterizations.