The ground-state rotational spectra of the three isotopomers H₃¹⁴N···I³⁵Cl, H₃¹⁴N···I³⁷Cl and H₃¹⁵N···I³⁵Cl of a symmetric-top complex formed between ammonia and iodine monochloride were detected and measured by using the pulsed-jet, Fourier-transform microwave technique in combination with a fast-mixing nozzle. The spectroscopic constants B₀, D_J, D_JK, χ(¹⁴N), χ(I), χ(Cl), M_aa(I) and M_bb(I) were determined for each isotopomer. Various of these constants were interpreted with the aid of simple models to give the geometry, the binding strength, and the electric charge redistribution relative to the free molecules NH₃ and ICl. The equilibrium geometry is one of C_3v symmetry, with the nuclei in the order H₃N···ICl and with the distance r(N···I)=2.711(2) Å. The intermolecular stretching force constant k_σ=30.4(3) N m^-1 is large and indicates that the complex is strongly bound. The changes in the halogen nuclear quadrupole coupling constant χ(I) and χ(Cl) from their respective free molecule values lead to the conclusion that the intermolecular electronic charge transfer, δ₁e^-, from N to I on complex formation is 0.078(8) e^-, while the polarization of the ICl subunit can be represented by a transfer, δ₂e^-, of 0.150(3) e^- from I to Cl. The net change at I is -0.073(5) e^-. A comparison of r(N···X), δ₂ and k_σ for the series of complexes H₃N···XY, where XY=Cl₂, Br₂, BrCl, ICl or ClF, is presented and some general conclusions are drawn.