From single-crystal Al-27 NMR experiments, the full tensors for both the electrical field gradient (EFG) and the chemical shift (CS) for the aluminum atoms in gamma-LiAlO2 have been determined. A simultaneous fit of the quadrupolar splittings observed for the four Al-27 in the unit cell gave the EFG tensor in the crystal frame, from which a quadrupolar coupling constant of chi = C-Q = 3.330 +/- 0.005 MHz and an asymmetry parameter of eta(Q) = 0.656 +/- 0.002 were derived. The experimentally determined quadrupolar splittings were sufficiently sensitive to quantify small deviations of both rotation axis direction and starting, direction by the data fitting routine. For determination of the CS tensor, the evolution of the outer satellite centers over the crystal rotation was trcked and the contribution of the quadrupolar shift was subtracted according to the previously determined EFG tensor. The resulting CS tensor of Al-27 yields an isotropic chemical shift of delta(iso) = 81.8 +/- 0.25 ppm and an asymmetry parameter of eta(CS) = 0.532 +/- 0.004, in good agreement with the fit of a MAS NMR spectrum acquired at B-0 = 21.1 T. From both experiments and DFT calculations using the CASTEP code, we find the eigenvectors of the EFG and CS tensors to be practically colinear.