Rotational spectra of the Ar-3-NH3 van der Waals tetramer were recorded between 4 and 17 GHz using a pulsed jet Fourier transform microwave spectrometer. Five isotopomers, namely Ar-3-NH3, Ar-3-(NH3)-N-15, Ar-3-ND3, Ar-3-ND2H, and Ar-3-NDH2, were studied and the spectra observed are characteristic of oblate symmetric tops. The transitions were assigned to three different K progressions, K=0, K=3, and K=6 of the ground internal rotor state of the complex. A small inversion tunneling splitting was observed for each of the deuterium containing isotopomers. For Ar-3-NH3 and Ar-3-(NH3)-N-15, one of these inversion components has a spin statistical weight of zero in the ground state and is, therefore, not observed. The N-14 quadrupole hyperfine structure was resolved and included in the fit of the spectroscopic constants for each of the N-14 containing isotopomers. The resulting spectroscopic constants were used to estimate the structure of the complex. Furthermore, the N-14 nuclear quadruple coupling constants and the inversion tunneling splittings observed for the various isotopomers contain information about the dynamics of the ammonia subunit within the Ar-3-NH3 complex.