The bond lengths, vibrational frequencies, and bond dissociation energies of the heavy and superheavy hydrogen halides HBr, HI, HAt and H[117] ([117] = element 117) have been calculated by using multireference relativistic configuration interaction (MR-RCI) and coupled-cluster [CCSD(T)] electronic structure methods. The effects of spin-orbit coupling on the coupled-cluster calculations were approximated by adding a correction term that represents the spin-orbit effect on the energy in the MR-RCI calculations, The calculated values are in good accord with the available experimental and theoretical data for HBr, HI, and HAt, with the latter predicted to have a bond length of 1.74 Angstrom and a dissociation energy of 1.37 eV via the corrected CCSD(T) calculations. By using the same method, H[117] is predicted to have a bond length of 1.94 Angstrom, a vibrational frequency of 1648 cm(-1), and a dissociation energy of 2.21 eV; i.e., it is predicted to have a significantly longer but only marginally weaker bond than HAt. This prediction is explained via strong spin-orbit effects, which cause the 8s orbital of [117] to be involved in the bonding.