The inelastic neutron scattering results and their analysis unequivocally point to a dominant Kitaev interaction in the honeycomb-lattice cobaltate BaCo₂(AsOH₄O)₂. Our anisotropic-exchange model closely describes all available neutron scattering data in the material's field-polarized phase. The density-matrix renormalization group results for our model are in close accord with the unusual double-zigzag magnetic order and the low in-plane saturation field of BaCo₂(AsOH₄O)₂.