  We show how the chiral properties of Bose Einstein condensates subject to
current-density interactions and loaded in optical lattices can be observed in
the realization of nonlinear Bloch states, whose spectrum lacks the usual
periodic structure. Chirality is also manifested by spatially localized states,
or gap solitons, which are found for positive rotation rates of the lattice at
the energy gaps between the linear energy bands, whereas for negative rotations
they appear in the semi-infinite gap of the linear spectrum. The stability of
extended and localized states is checked through the spectrum of linear
excitations and nonlinear time evolution of perturbed states, and the
phenomenon of Bloch oscillations is explored. Our results are obtained in quasi
1D ring geometries with feasible experimental parameters.
