High-resolution powder neutron diffraction data (HRPD, ISIS Facility. U.K.) were collected on (H3O)Zr-2(PO4)(3) between 4 and 300 K. In the range 175-180 K, a ferroelastic first-order phase transition from the rhombohedral R(3) over bar c NASICON structure to a monoclinic distorted one was discovered. Rietveld structure refinements were performed at 300 K (a = 8.74848(3), c = 23.7598(1) Angstrom) and 4.5 K (space group C2/c or Cc, a = 15.0663(1), b = 8.7878(1), c = 9.3611 (1) Angstrom, beta = 122.498(1)degrees). At RT, the hydronium ion H3O- is pyramidal disordered over two inversion-related configurations. At LT, H3O+ becomes nearly planar, with two H atoms ordered and hydrogen-bonded to neighboring oxygens, and the third H atom disordered over two close positions with 2/3 and 1/3 statistical occupancies. Relations with the structural features of hydronium in other structures and the nature of order-disorder are discussed. An atomistic mechanism for proton conductivity is proposed.