The zz component of the molecular quadrupole moment Theta of ammonia is computed at the restricted Hartree-Fock and coupled cluster theory with singles and doubles (CCSD) levels of approximation as a function of the symmetric stretching and inversion motions, considering a wide range of values for the corresponding vibrational coordinates (z is the threefold symmetry axis). Using these results and the nonrigid invertor rovibrational wave functions, effective molecular quadrupole moments are obtained for the low lying roinversional states of (NH3)-N-14. The predicted values exhibit a sizable and nonmonotonic dependence on the corresponding inversional (upsilon(2)) and rotational (J,k) quantum numbers. The calculated effective quadrupole moments for the vibrational (inversional) ground states (upsilon(2) = 0(+/-)) are found to be about 10% smaller in absolute value than the two available experimental results [-2.42 +/- 0.04 a.u.; J. G. C. M. van Duijneveldt-van de Rijdt and F. B. van Duijneveldt, J. Mel. Struct. (THEOCHEM) 89, 185 (1982) and -2.45 +/- 0.3 a.u.; S. G. Kukolich, Chem. Phys. Lett. 5, 401 (1970); 12, 216 (1971) (E)]. Our CCSD value of the quadrupole moment pertaining to the equilibrium geometry is in a very close agreement with the best theoretical values that are available in the literature. This fact and the high quality of the roinversional wave functions that were employed lead us to believe that our theoretical predictions may be more accurate than their experimental counterparts. In particular, the difference between the theoretical and experimental values casts doubt on the reliability of the error bars (+/- 0.04 a.u.) in one of the experimental results quoted above.