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It is well established that the anomalous Hall effect displayed by a ferromagnet scales with its magnetization. Therefore, an antiferromagnet that has no net magnetization should exhibit no anomalous Hall effect. We show that the noncolinear triangular antiferromagnet Mn₃Ge exhibits a large anomalous Hall effect comparable to that of ferromagnetic metals; the magnitude of the anomalous conductivity is ~500 (ohm·cm)⁻¹ at 2 K and ~50 (ohm·cm)⁻¹ at room temperature. The angular dependence of the anomalous Hall effect measurements confirms that the small residual in-plane magnetic moment has no role in the observed effect except to control the chirality of the spin triangular structure. Our theoretical calculations demonstrate that the large anomalous Hall effect in Mn₃Ge originates from a nonvanishing Berry curvature that arises from the chiral spin structure, and that also results in a large spin Hall effect of …