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Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moiré materials provide a highly tuneable platform for studies of electron correlation^{, , , , , , , , , , –}. Correlation-driven phenomena, including the Mott insulator^{, , –}, generalized Wigner crystals^,,, stripe phases and continuous Mott transition^,, have been demonstrated. However, non-trivial band topology has remained unclear. Here we report the observation of a quantum anomalous Hall effect in AB-stacked MoTe₂ /WSe₂ moiré heterobilayers. Unlike in the AA-stacked heterobilayers, an out-of-plane electric field not only controls the bandwidth but also the band topology by intertwining moiré bands centred at different layers. At half band filling, corresponding to one particle per moiré unit cell, we observe quantized Hall resistance, h/e² (with h and e denoting the Planck’s constant and electron charge …