Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the u=½ fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultracold polar molecules trapped in a deep optical lattice. With the motion of the molecules pinned, under certain conditions, these rotational excitations form a fractional Chern insulating state. We present a detailed experimental blueprint for its realization and demonstrate that the implementation is consistent with near-term capabilities. Phys. Rev. Lett. 109, 266804 (2012); Phys. Rev. Lett. 110, 185302 (2013).
