The effect of deuteration on the motion of ammonium ions and/or the structural phase transition in NH₄AuCl₄ was studied by means of ³⁵Cl nuclear quadrupole resonance measurements. The transition temperature shifted by 5 K from 28.5 K for NH₄AuCl₄ to 33.5 K for ND₄AuCl₄. Spin-lattice relaxation caused by the modulation of the electric field gradient due to the motion of nearby ammonium ions was observed. The activation energy of the motion of the ammonium ions was determined to be 0.8 and 1.8 kJ mol^-1 for NH₄AuCl₄ and ND₄AuCl₄, respectively. By the use of the simple harmonic oscillator model, the barrier height V₀ and the number of wells n of the potential for the reorientation of the ammonium ions were determined as V₀ = 4.2 kJ mol^-1 and n = 4 from the above activation energies for the NH₄⁺ and ND₄⁺ reorientations.