We report on the successful growth of beta -Ga2O3 single crystals using the Czochralski method. Model calculations show that the gas phase consists of Ga2O, GaO or Ga independent of the ratio of oxygen and Ar or N-2. We find that for growing single crystals the evaporation has to be suppressed by a finite amount of oxygen. A CO2/Ar gas atmosphere was found to meet this requirement.