(CuI)(3)P4S4 is obtained by reaction of stoichiometric amounts of CuI, P, and S in evacuated silica ampoules. The yellow compound consists of monomeric beta-P4S4 cage molecules that are separated by hexagonal columns of CuI. (CuI)(3)P4S4 crystallizes isotypic to (CuI)(3)P4Se4 in the hexagonal system, space group P6(3)cm (no. 185) with a = 19.082(3), c = 6.691 (1) Angstrom, V = 2109.9(6) Angstrom(3), and Z=6. Three of the four phosphorus atoms are bonded to copper, whereas no bonds between copper and sulfur are observed. The two crystallographically distinct copper sites are clearly differentiated by Cu-65 magic-angle spinning (MAS) NMR spectroscopy. Furthermore, an unequivocal assignment of the P-31 MAS-NMR spectra is possible on the basis of homo- and heteronuclear dipole-dipole and scalar interactions. Dipolar coupling to the adjacent quadrupolar spins Cu-63 65 generates a clear multiplet structure of the peaks attributable to P1 and P2, respectively. Furthermore, the utility of a newly developed two-dimensional NMR technique is illustrated to reveal direct connectivity between P atoms based on (P-31-P-31) scalar interactions.