The structure and ground state dynamics of the atom-diatom interaction between Kr and HI has been investigated by pulsed-nozzle Fourier-transform microwave spectroscopy. The ground state of Kr-84-IH is shown to have R-cm = 4.0526(1) Angstrom, theta = 152.87(1)degrees while R-cm = 4.0195(1) Angstrom, theta = 158.85(1)degrees for Kr-84-ID. The potential surface from an ab initio molecular orbital calculation was scaled and shifted to yield a non-linear least-squares fit of the rovibrational state energies to the experimental data. The ground state, Kr-IH isomeric structure is similar to Ar-IH but contrasts with other members of the homologous series Kr-HX (X=F, Cl and Br).