  We propose a new mechanism for quantum anomalous Hall (QAH) effect in the AB
stacked MoTe$_2$/WSe$_2$ system. Based on the observation that the inter-layer
tunneling is suppressed in the AB stacking, we consider a model with two layers
coupled through the Coulomb interaction. The moir\'e lattices of the two layers
are shifted to form a honeycomb lattice together. Initially, the system is in a
layer-polarized Mott insulator at $\nu_T=1$. But with a displacement field, an
equal number of holes and electrons are doped into the two layers respectively
and they form inter-layer exciton condensation. Through mean field theory, we
find p$\pm$ip exciton condensation in a certain parameter regime, which leads
to a Chern insulator with Chern number $C=\pm 1$. The valleys are polarized due
to the kinetic energy instead of interaction. But the polarization in the two
layers can be either the same or opposite depending on small perturbations away
from a symmetric point. As a result, both valley polarized and inter-valley
coherent (IVC) Chern insulator phases are possible. The latter has the same
spin $S_z$ in the two layers.
