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The new compound H3P⋯AgI has been synthesized in the gas phase by means of the reaction of laser-ablated silver metal with a pulse of gas consisting of a dilute mixture of ICF3 and PH3 in argon. Ground-state rotational spectra were detected and assigned for the two isotopologues H3P⋯107AgI and H3P⋯109AgI in their natural abundance by means of a chirped-pulse, Fourier-transform, microwave spectrometer. Both isotopologues exhibit rotational spectra of the symmetric-top type, analysis of which led to accurate values of the rotational constant B0, the quartic centrifugal distortion constants DJ and DJK, and the iodine nuclear quadrupole coupling constant χaa(I) = eQqaa. Ab initio calculations at the explicitly-correlated level of theory CCSD(T)(F12∗)/aug-cc-pVDZ confirmed that the atoms P⋯Ag-I lie on the C3 axis in that order. The experimental rotational constants were interpreted to give the bond lengths r0(P⋯Ag) = 2.3488(20) Å and r0(Ag-I) = 2.5483(1) Å, in good agreement with the equilibrium lengths of 2.3387 Å and 2.5537 Å, respectively, obtained in the ab initio calculations. Measures of the strength of the interaction of PH3 and AgI (the dissociation energy De for the process H3P⋯AgI = H3P + AgI and the intermolecular stretching force constant FP⋯Ag) are presented and are interpreted to show that the order of binding strength is H3P⋯HI < H3P⋯ICl < H3P⋯AgI for these metal-bonded molecules and their halogen-bonded and hydrogen-bonded analogues.