AbstractChern 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 numberCthat defines the quantized Hall conductance asSxy = Ce2/h. IncreasingCis pivotal for the realization of low-power-consumption topological electronics, but there has been no clear-cut solution to this problem so far, with the majority of existing Chern insulators showingC = 1. Here, by using state-of-the-art theoretical methods, we propose an efficient approach for the realization of the high-Cstate in MnBi2Te4/hBN van der Waals multilayer heterostructures. We show that a stack ofnMnBi2Te4films withC = 1 intercalated by hBN monolayers gives rise to a high Chern number state withC = n, characterized bynchiral edge modes. This state can be achieved both under the external magnetic field and without it, both cases leading to the quantized Hall conductanceSxy = Ce2/h. Our results, therefore, pave the way to practical high-Cquantized Hall systems.