The interaction of water with the BaF2(111) single crystal surface is investigated using the helium atom scattering technique. It is found that H2O forms a long-range ordered two-dimensional (2D) phase with (1 x 1) translational symmetry already after an exposure of 3 L (1 L=10(-6) Torr s) at temperatures below 150 K. The activation energy for desorption of the saturated 2D phase, which is assigned to a bilayer, is estimated to be 46+/-2 kJ mol(-1), corresponding to a desorption temperature of 165 K. The desorption of multilayers was observed at 150 K, consistent with a binding energy of 42+/-2 kJ mol(-1). Before completion and after desorption of the saturated 2D phase, a superstructure consistent with a disordered (square root of 3 x square root of 3)R30 degrees lattice has been observed, which is attributed to the first layer of water with a coverage of one molecule per surface unit cell, in accordance with recent theoretical studies. Desorption of this phase is observed at temperatures above 200 K, consistent with an unexpectedly strong bonding of the molecules to the substrate.