Using our newly developed particle swarm optimization algorithm on crystal structural prediction, we characterized the pressure-induced structural transition sequence of gallane (GaH${}_{3}$). As has been observed in alane (AlH${}_{3}$), enthalpy calculations reveal that the $\mathrm{Pm}$$\overline{3}$$n$ structure of GaH${}_{3}$ becomes stable above 160 GPa, below which it is unstable with respect to elemental decomposition. Interestingly, the $\mathrm{Pm}$$\overline{3}$$n$ structure is metallic, and the application of the Allen-Dynes modified McMillan equation reveals a high superconducting transition temperature (${T}_{\mathrm{c}}$), which reaches 86 K at 160 GPa and increases with decreasing pressure (${T}_{c}$ $=$ 102 K at 120 GPa). Our band structure calculations demonstrate that GaH${}_{3}$ within the $\mathrm{Pm}$$\overline{3}$$n$ structure is a highly ionic solid, where the ionicity of H atoms plays an important role in the predicted high temperature superconductivity.