Core-level spectra of individual heteroepitaxial nanocrystals were measured with a spectroscopic photoemission and low-energy electron microscope that allows laterally resolved photoemission spectroscopy. The nanocrystals were obtained by depositing nominally 2 monolayers (ML) of InAs on a Se-terminated GaAs(001) surface. The Se-termination of GaAs results in the formation of a 2-3-ML-thick film of Ga2Se3 on top of bulk GaAs. During heteroepitaxy the InAs reacts with the Ga2Se3: A phase separation takes place on the anion sublattice, while an alloying takes place on the cation sublattice. During the initial stages of growth, a submonolayer-thick wetting layer of InxGa1-xAs is formed that is covered by (InyGa1-y)2Se3. (InyGa1-y)2Se3-covered InAs nanocrystals are formed on this surface.