  I introduce and analyse chiral light--matter interaction in the ultrastrong
coupling limit where the rotating-wave approximation cannot be made. Within
this limit, a two-level system (TLS) with a circularly polarized transition
dipole interacts with a copolarized mode through rotating-wave terms. However,
the counter-rotating terms allow the TLS to couple to a counter-polarized mode
with the same coupling strength, i.e., one that is completely decoupled within
the rotating-wave approximation. Although such a Hamiltonian is not particle
number conserving, the conservation of angular momentum generates a $U(1)$
symmetry which allows constructing an ansatz. The eigenstates and dynamics of
this novel model are computed for single-cavity interactions and for a
many-mode system. The form of the ansatz provides significant analytic insight
into the physics of the ground state and the dynamics, e.g., it indicates that
the ground states are two-mode squeezed. This work has significant implications
for engineering light--matter interaction and novel quantum many-body dynamics
beyond the rotating-wave approximation.
