The electronic structure of the heavy diatomic molecule BaI has been examined for the first time by ab initio multiconfigurational configuration interaction (MRCI) and coupled cluster (RCCSD(T)) methods. The effects of special relativity have been taken into account through the second-order Douglas - Kroll- Hess approximation. The construction of Omega(omega,omega) potential energy curves allows for the estimation of "experimental" dissociation energies (D,) of the first few excited states by exploiting the accurately known D, experimental value of the X-2 Sigma(+) ground state. All states examined are of ionic character with a Mulliken charge transfer of 0.5 e(-) from Ba to 1, and this is reflected to large dipole moments ranging from 6 to 11 D. Despite the inherent difficulties of a heavy system like Bal, our results are encouraging. With the exception of bond distances that on the average are calculated 0.05 angstrom longer than the experimental ones, common spectroscopic parameters are in fair agreement with experiment, whereas De values are on the average 10 kcal/mol smaller.