  Recent experiments reported the realization of a heavy Fermi liquid in
AB-stacked MoTe$_2$/WSe$_2$ heterobilayers. In this paper we show that the
AB-stacked heterobilayer configuration is particularly suited to realize
topological Kondo semimetal and topological Kondo insulator ground states at a
doping of two holes per moir\'e unit cell. The small lattice mismatch between
the MoTe$_2$ and WSe$_2$ monolayers and the different bandwidths of their
highest lying moir\'e valence bands means that, in the experimentally relevant
range of hole dopings, the MoTe$_2$ layer is effectively a Mott insulator with
only low-lying magnetic excitations Kondo-coupled to more itinerant electrons
in the WSe$_2$. The crucial consequence of the AB-stacking configuration is
that the interlayer tunnelling connects orbitals of opposite parity in the two
layers, leading to a chiral Kondo coupling. We show that the chiral Kondo
coupling favors a topological Kondo semimetal at filling $\nu=1+1$, with a
non-quantized spin Hall conductance arising from edge modes, whose spectrum and
overlap with bulk states we determine. We further show that a spatially random
strain field that locally breaks the rotation symmetry can convert the Kondo
semimetal to a narrow gap topological Kondo insulator featuring a quantized
spin Hall conductance.
