We measured the spin state of iron in ferropericlase (Mg0.83Fe0.17)O at high pressure and found a high-spin to low-spin transition occurring in the 60- to 70-gigapascal pressure range, corresponding to depths of 2000 kilometers in Earth's lower mantle. This transition implies that the partition coefficient of iron between ferropericlase and magnesium silicate perovskite, the two main constituents of the lower mantle, may increase by several orders of magnitude, depleting the perovskite phase of its iron. The lower mantle may then be composed of two different layers. The upper layer would consist of a phase mixture with about equal partitioning of iron between magnesium silicate perovskite and ferropericlase, whereas the lower layer would consist of almost iron-free perovskite and iron-rich ferropericlase. This stratification is likely to have profound implications for the transport properties of Earth's lowermost mantle.