  We present a new tractable quantum Rabi model for $N$-level atoms by
extending the $\mathbb Z_2$ symmetry of the two-state Rabi model. The
Hamiltonian is $\mathbb Z_N$ 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 {\em chiral}, which makes it differ from any
existing $N$-state Rabi models in the literature. The $\mathbb Z_N$ 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
$N$-fold degenerate. For the three-state case ($N=3$), we obtain three
transcendental functions whose zeros give the regular (i.e. non-exceptional)
energies of the model.
