Single-crystal neutron diffraction shows that ice IX, the low-temperature modification of ice III, has an almost completely proton-ordered structure in which the ordered component contains two types of water molecules, type 1 in a site of no point symmetry, and type 2 on a twofold axis, each forming four hydrogen bonds in a three-dimensional framework. The configuration of the water molecules is slightly but significantly altered from that of water vapor. Independent O-D distances, which do not differ significantly from one another, average 0.982± 0.003 Å (corrected for thermal motion), and are increased by 0.012 Å over the vapor value. The shift in O-D stretching frequency ν1 from vapor to ice IX corresponds to a slope dν1/dr≅ -20 000 cm-1. Å-1, which agrees with the slope predicted from spectroscopic anharmonicity constants. D-O-D bond angles (104.7± 0.4°, 106.0± 0.2°) are not decreased from the vapor value (104.5°) despite the smaller O... O... O angles into which the water molecules donate protons (98.2°, 100.8°); the same effect occurs also in ice II and oxalic acid dihydrate. The ordered molecules are oriented into the available O... O... O angles that differ the least from 104.5°, but the orientation is not completely symmetrical in relation to these angles so that the H-bond bend angles are substantially larger than the minimum possible. Observed amplitudes of thermal vibration, interpreted in terms of rigid-body motion of the molecules, indicate that restoring forces for H-bond distortion are approximately isotropic, ignoring the low-symmetry molecular environments. The amplitudes correspond to appropriate average vibrational frequencies. About 4% of the deuterons in the structure are not in the ordered sites, but occupy the alternative sites that also provide hydrogen bonding. The retention of this partial disorder may be an effect of quenching through the transition range from ice III to ice IX, or it may be an inherent feature of the ice IX structure as achievable experimentally.