The 400-km seismic discontinuity has traditionally been ascribed to the isochemical transformation of α-olivine to the β-modified-spinel structure in a mantle of peridotitic bulk composition1-6. It has recently been proposed7,8 that the observed seismic velocity increase at 400km depth is too abrupt and too small to result from a phase change in olivine but instead requires that the transition zone be chemically distinct in bulk composition from the uppermost mantle. By requiring phase relations in the Mg2SiO4-Fe2SiO4 system to be internally consistent thermodynamically, we find that the α-β transition in olivine of mantle (Mg0.9Fe0.1) 2SiO4 composition is extremely sharp, occurring over a depth interval (isothermal) of ∼6 km. The magnitude of the predicted velocity increase is in agreement with that observed seismically9,10 if the transition zone is composed of ∼60-70% olivine. Thus, our results indicate that seismic velocities across the 400-km discontinuity are consistent with a transition zone of homogeneous peridotitic composition and do not require chemical stratification.