We present a theoretical estimate of the reaction probability γ for the chlorine nitrate (ClONO2) hydrolysis on type II (water-ice) polar stratospheric cloud material. This estimate is based on high-level ab initio calculations in a supermolecule containing four molecules of water and one molecule of chlorine nitrate. To the best of our knowledge, this is the first estimate of γ that makes no a priori use of experimental data at all. Instead, the rate constants for association, surface reaction, and surface desorption as calculated by variational transition state theory enter the model. At 180 K we estimate γ ≈ 0.10-0.06+0.20, which is within the error bars of the agreeing recommendations of Jet Propulsion Laboratory and International Union of Pure and Applied Chemistry of 0.3-0.1+0.7. The temperature dependence between 75 and 150 K agrees with results obtained from laser-induced thermal desorption. In particular, the temperature of 105 K above which γ becomes less than unity is reproduced well. A negative temperature dependence between 180 and 210 K is found, which has not yet been confirmed in the laboratory for ClONO2 hydrolysis but only for BrONO2 on ice. This qualitative agreement of a gas-phase cluster calculation with experiments on hexagonal ice surfaces implies that a highly mobile and oxygen disordered ice surface rather than an ordered, immobile crystalline ice surface is experienced by chlorine nitrate molecules under polar stratospheric conditions.