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 84Kr–IH is shown to have Rcm=4.0526(1) Å, θ=152.87(1)° while Rcm=4.0195(1) Å, θ=158.85(1)° for 84Kr–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).