The triclinic form of AlPO4-34, a microporous aluminophosphate with the chabazite (CHA) topology, adopts a rhombohedral symmetry upon calcination. The framework structure of this phase remains intact under ambient conditions, but it distorts dramatically, though reversibly, in the presence of water. Following these structural changes in situ by X-ray diffraction revealed that there are actually two stable rehydrated phases, which differ from each other by one water molecule in the channel. Both of these phases have triclinic unit cells that are closely related to that of the calcined rhombohedral phase. The structure of the low-temperature (10 degrees C), fully rehydrated phase (phase B) was elucidated by combining high-resolution synchrotron powder diffraction with solid-state NMR techniques. Coordination of three of the six Al atoms to water molecules causes the deformation of the framework and the reduction of the symmetry. Rietveld refinement of the structure of phase B in the triclinic space group P1 (a = 9.026, b = 9.338, c = 9.508 Angstrom, alpha = 95.1 degrees, beta = 104.1 degrees, and gamma = 96.6 degrees) converged with R-F = 0.079 and R-WP = 0.176 (R-exp = 0.087). Framework connectivities derived from the structure were used to assign P-31 NMR lines as well as part of the Al-27 NMR signal.