A solid-state P-31 CP/MAS NMR study of the 1:1 adduct, 1, of indium tribromide and a triarylphosphine permits the first unambiguous measurement of (1)J(In-115,P-31). The large quadrupole moment of In-115 (spin 9/2) generally makes such measurements impossible in solution NMR studies. Analysis of a P-31 NMR spectrum of a nonspinning powder sample of 1 indicates that the (1)J(In,P) tenser is anisotropic (J(parallel to) = 1896 +/- 150 Hz, J(perpendicular to) = 716 +/- 150 Hz), implicating Contributions from mechanisms other than the commonly accepted Fermi-contact mechanism.