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We present a new tractable quantum Rabi model for $N$-level atoms byextending the $\mathbb Z_2$ symmetry of the two-state Rabi model. TheHamiltonian is $\mathbb Z_N$ symmetric and allows the parameters in the levelseparation terms to be complex while remaining hermitian. This latter propertymeans that the new model is {\em chiral}, which makes it differ from anyexisting $N$-state Rabi models in the literature. The $\mathbb Z_N$ symmetryprovides partial diagonalization of the general Hamiltonian. The exact isolated(i.e. exceptional) energies of the model have the Rabi-like form but are$N$-fold degenerate. For the three-state case ($N=3$), we obtain threetranscendental functions whose zeros give the regular (i.e. non-exceptional)energies of the model.

$Z_N$ symmetric chiral Rabi model: a new $N$-level system