  Chern insulators are two-dimensional magnetic topological materials that
conduct electricity along their edges via the one-dimensional chiral modes. The
number of these modes is a topological invariant called the first Chern number
$C$, that defines the quantized Hall conductance as $S_{xy}= C e^2/h$.
Increasing $C$ is pivotal for the realization of low-power-consumption
topological electronics, but there has been no clear-cut solution of this
problem so far, with the majority of existing Chern insulators showing $C=1$.
Here, by using state-of-the-art theoretical methods, we propose an efficient
approach for the realization of the high-$C$ Chern insulator state in
MnBi$_2$Te$_4$/hBN van der Waals multilayer heterostructures. We show that a
stack of $n$ MnBi$_2$Te$_4$ films with $C=1$ intercalated by hBN monolayers
gives rise to a high Chern number state with $C=n$, characterized by $n$ chiral
edge modes. This state can be achieved both under the external magnetic field
and without it, both cases leading to the quantized Hall conductance $S_{xy}= C
e^2/h$. Our results therefore pave way to practical high-$C$ quantized Hall
systems.
