A single-crystal Ga-71 NMR study of the garnet Y3Ga5O12 (YGG) has resulted in the determination of the first chemical shielding tensors reported for the Ga-71 quadrupole. The single-crystal spectra are analyzed in terms of the combined effect of quadrupole coupling and chemical shielding anisotropy (CSA). Ga-71 quadrupole coupling and CSA parameters for the two (tetrahedrally and octahedrally coordinated) gallium sites with axial symmetry in YGG (Ga-IV, C-Q = 13.1 +/- 0.2 MHz and delta(sigma) = 54 +/- 50 ppm; Ga-VI, C-Q = 4.10 +/- 0.06 MHz and delta(sigma) = 24 +/- 3 ppm) are fully consistent with its cubic crystal structure which supports the reliability of the experimental data. In addition, the Ga-71 and Al-27 isotropic chemical shifts for YGG and YAG give further support to the linear correlation observed earlier between Ga-71 and Al-27 isotropic chemical shifts.