Crystalline single-phase LiHf2(PO4)(3) has been synthesized. It shows a phase transition at 235 K that has been characterized through DSC, low-temperature X-ray diffractometry, and ionic conductivity measurements. The crystal structures of the two phases have been established by neutron powder diffraction at 175 and 320 K. The room-temperature phase is rhombohedral R(3) over barc$, Z = 6, a = 8.8306(1) Angstrom and c = 22.0270(5) Angstrom and the structure has been refined by the Rietveld method to R-wp = 6.29% and R-F = 4.68%. The framework is similar to that shown by NASICON materials with the Li cations disordered out of the M1 position and close to the M1-M2 bottleneck site. The crystallographically refined composition was Li0.87Hf2.032(PO4)(3) in agreement with the chemical analysis. The low-temperature phase is triclinic C (1) over bar, Z = 4, a = 15.2680(4) Angstrom, b = 8.6946(3), c = 9.0722(2) Angstrom, alpha = 89.323(2)degrees, beta = 123.740(2)degrees, and gamma = 90.666(2)degrees, and the structure has been refined to R-wp = 4.61% and R-F = 2.25%. This is a common reversible order-disorder phase transition with some subtle structural changes. These structural changes and the consequences in the ionic conductivity properties will be discussed. This is the first structural report on a low-temperature phase in the Li-NASICON system.