We present a new tractable quantum Rabi model for NN-level atoms by extending the Z2Z2 symmetry of the two-state Rabi model. The Hamiltonian is ZNZN symmetric and allows the parameters in the level separation terms to be complex while remaining hermitian. This latter property means that the new model is chiral , which makes it differ from any existing NN-state Rabi models in the literature. The ZNZN symmetry provides partial diagonalization of the general Hamiltonian. The exact isolated (i.e. exceptional) energies of the model have the Rabi-like form but are NN-fold degenerate. For the three-state case (N=3N=3), we obtain three transcendental functions whose zeros give the regular (i.e. non-exceptional) energies of the model.