  If an extensive partition in two dimensions yields a gapful entanglement
spectrum of the reduced density matrix, the Berry curvature based on the
corresponding entanglement eigenfunction defines the Chern number. We propose
such an entanglement Chern number as a useful, natural, and calculable
topological invariant, which is potentially relevant to various topological
ground states. We show that it serves as an alternative topological invariant
for time-reversal invariant systems and as a new topological invariant for a
weak topological phase of a superlattice Wilson-Dirac model. In principle, the
entanglement Chern number can also be effective for interacting systems such as
topological insulators in contrast to $Z_2$ invariants.
