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The layered antiferromagnetic MnBi₂Te₄ films have been proposed to be an intrinsic quantum anomalous Hall (QAH) insulator with a large gap. It is crucial to open a magnetic gap of surface states. However, recent experiments have observed gapless surface states, indicating the absence of out-of-plane surface magnetism, and thus, the quantized Hall resistance can only be achieved at the magnetic field above 6 T. We propose to induce out-of-plane surface magnetism of MnBi₂Te₄ films via the magnetic proximity with magnetic insulator CrI₃. A strong exchange bias of ∼40 meV originates from the long Cr-e_g orbital tails that hybridize strongly with Te p orbitals. By stabilizing surface magnetism, the QAH effect can be realized in the MnBi₂Te₄/CrI₃ heterostructure. Moreover, the high–Chern number QAH state can be achieved by controlling external electric gates. Thus, the MnBi₂Te₄/CrI₃ heterostructure provides …