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The quantum anomalous Hall effect1,2is a fundamental transport response of a topological insulator in zero magnetic field. Its physical origin is a result of an intrinsically inverted electronic band structure and ferromagnetism3, and its most important manifestation is the dissipationless flow of chiral charge currents at the edges of the system4, a property that has the potential to transform future quantum electronics5,6. Here, we report a Berry-curvature-driven4,7anomalous Hall regime at temperatures of several Kelvin in the magnetic topological bulk crystals in which Mn ions self-organize into a period-ordered MnBi2Te4/Bi2Te3superlattice. Robust ferromagnetism of the MnBi2Te4monolayers opens a surface gap8–10, and when the Fermi level is tuned to be within this gap, the anomalous Hall conductance reaches an e2/hquantization plateau, which is a clear indication of chiral transport through the edge states. The quantization in this regime is not obstructed by the bulk conduction channels and therefore should be present in a broad family of topological magnets.