Chlorofluorocarbons (CFCs), along with bromine compounds, have been unequivocally identified as being responsible for most of the anthropogenic destruction of stratospheric ozone. With curbs on emissions of these substances, the recovery of the ozone layer will depend on their removal from the atmosphere. As CFCs have no significant tropospheric removal process, but are rapidly photolysed above the lower stratosphere, the timescale for their removal is set mainly by the rate at which air is transported from the troposphere into the stratosphere. Using a global climate model we predict that, in response to the projected changes in greenhouse-gas concentrations during the first half of the twenty-first century, this rate of mass exchange will increase by 3% per decade. This increase is due to more vigorous extra-tropical planetary waves emanating from the troposphere. We estimate that this increase in mass exchange will accelerate the removal of CFCs to an extent that recovery to levels currently predicted for 2050 and 2080 will occur 5 and 10 years earlier, respectively.