A reversible first-order phase transition has been found around 0 degrees C in the compound LiHf2(PO4)(3), which has been followed by DSC, XRD, NMR (P-31 and Li-7), and impedance techniques. In the low-temperature phase, a triclinic distortion of the NASICON framework has been detected for the first time in the LiM2(PO4)(3) family. In this phase location of lithium ions at low-symmetry sites (probably M-2 sites) has been deduced from Li-7 NMR data. Above 0 degrees C, the usual NASICON symmetry (rhombohedral R (3) over bar c) is recovered and an abrupt increase of the ionic mobility is observed: activation energy obtained from bulk de conductivity decreases from 1.39 to 0.33 eV. From NMR data, a strong delocalization of lithium ions over M-1 and M-2 sites is detected when going from the triclinic to the rhombohedral phase.