This paper presents a model for the thermal and chemical evolution of a global magma ocean created by impact heating during the earth's accretion. Detailed calculations are given for a melt depth of 120 km for end member picritic and periodotitic compositions. Application of fluid mechanics and heat transfer principles shows as a first approximation that the chemical evolution can be portrayed by idealized fractional crystallization occurring only on the bottom of the magma ocean. The fractional crystallization sequence for the picritic model is 90 km of mafics overlain by 15 km of ol-spgabbronorite and topped by 15 km of iron-rich leucodiorite; whereas the periodotite sequence consists of 99 km of dunite, harzburgite, and websterite overlain by 5 km of Ol-sp-gabbronorite and capped by 16 km of ferroleucogabbronorite. Although subsolidus convection would rehomoginize all but the felsic layers of the picritic model, the layers of the periodotite would remain intact owing to their stable density profile. The mineralogy of the felsic layers is largely independent of the basic model assumptions. However, the composition of the mafic layers is model dependent. The most likely results for the mafic-mafic layers (lherzolite or primitive mantle periodotite) are similar to mantle xenoliths, suggesting that a terrestrial magma ocean may have existed. However, comparison of the chemistry of the calculated upper felsic layer with that of the Canadian shield shows that crystallization of a global magma ocean would not directly produce the Archean continental crust. Multiple melting and differentiation of the Fe-leucodiorite to Fe-leucogabbronorite layer and of the underlying primitive mantle would be required to form an Archean granitoid crust.