  We demonstrate that a Chern insulator could be realized on a real
two-dimensional lattice of an organic Dirac semimetal {\alpha}-(BEDT-TTF)2I3 by
introducing potential and magnetic modulations in a unit cell. It is a
topologically-nontrivial insulator which shows the quantum Hall effect even at
zero magnetic field. We assumed a pattern of site potential and staggered
plaquette magnetic flux on the lattice so as to imitate the observed stripe
charge ordering pattern. When the magnetic modulation is sufficiently large,
the system becomes a Chern insulator, where Berry curvatures around two gapped
Dirac cones have the same sign on each band, and one chiral edge state connects
the conduction and valence bands at each crystal edge. The present model is an
organic version of Haldane's model, which discussed the Chern insulator on the
honeycomb lattice with second nearest neighbor couplings.
