  We investigate the influence of rotation on the dynamical chiral symmetry
breaking in strongly interacting matter. We develop a self-consistent
Bogoliubov-de Gennes-like theoretical framework to study the inhomogeneous
chiral condensate and the possible chiral vortex state in rotating finite-size
matter in four-fermion interacting theories. We show that for sufficiently
rapid rotation in $2+1$ dimensions, the ground state can be a chiral vortex
state, a type of topological defect in analogy to superfluids and
superconductors. The vortex state exhibits pion condensation, providing a new
mechanism to realize pseudoscalar condensation in strongly interacting matter.
