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Recent discovery of a phase transition from perovskite to post-perovskite suggests that the physical properties of Earth's lowermost mantle, called the D″ layer, may be different from those of the overlying mantle. We report that the electrical conductivity of (Mg_0.9Fe_0.1)SiO₃ post-perovskite is >10² siemens per meter and does not vary greatly with temperature at the conditions of the D″ layer. A post-perovskite layer above the core-mantle boundary would, by electromagnetic coupling, enhance the exchange of angular momentum between the fluid core and the solid mantle, which can explain the observed changes in the length of a day on decadal time scales. Heterogeneity in the conductivity of the lowermost mantle is likely to depend on changes in chemistry of the boundary region, not fluctuations in temperature.