The observed positive trends in Antarctic sea ice pose a challenge to our understanding of the climate system, in that one would expect sea ice to melt in a warming climate, as observed in the Arctic. In addition, global climate models participating in the Coupled Model Intercomparison Project (CMIP) Phases 3 and 5 are unable to simulate the observed positive trends. Recent single-forcing experiments where only stratospheric ozone is changed, show that ozone depletion causes negative sea ice trends and, conversely, that ozone recovery will mitigate the future sea ice loss associated with increasing greenhouse gases. Hence, over the observational period, models indicate that both greenhouses gases and ozone depletion would act in the same direction, and produce negative sea ice trends. However, investigation of trends in CMIP5 pre-industrial control model integrations reveals that both positive and negative trends, with amplitudes much larger than the one in the recent observation, can occur in the absence of forcing agents, solely as a consequence of internal climate variability. This suggests that the recently observed trends may be a reflection of such variability rather than of a response to anthropogenic forcings.