  We investigate a new class of topological antiferromagnetic (AF) Chern
insulators driven by electronic interactions in two-dimensional systems without
inversion symmetry. Despite the absence of a net magnetization, AF Chern
insulators (AFCI) possess a nonzero Chern number $C$ and exhibit the quantum
anomalous Hall effect (QAHE). Their existence is guaranteed by the bifurcation
of the boundary line of Weyl points between a quantum spin Hall insulator and a
topologically trivial phase with the emergence of AF long-range order. As a
concrete example, we study the phase structure of the honeycomb lattice
Kane-Mele model as a function of the inversion-breaking ionic potential and the
Hubbard interaction. We find an easy $z$-axis $C=1$ AFCI phase and a spin-flop
transition to a topologically trivial $xy$-plane collinear antiferromagnet. We
propose experimental realizations of the AFCI and QAHE in correlated electron
materials and cold atom systems.
