Coherent precipitation of Zn3P2 during Zn diffusion in a GaInAsP/InP heterostructure was studied using high-resolution transmission electron microscopy. Zn-diffusion-induced intermixing of Ga and In across the GaInAsP/InP heterointerface provided a Ga-mixed InP region which was nearly lattice-matched with Zn3P2 crystal and thus allowed thecoherent precipitation of Zn3P2. The Zn3P2 precipitates were preferentially nucleated at stacking faults which were formed to relax interfacial strain built up by the intermixing. The precipitates were grown to planar epitaxial layer along (100) plane in the lattice-matched region. The TEM images and diffraction pettern revealed that the tetragonal Zn3P2 crystals were coherently matched to the fcc structured GaInP matrix by the {{{{ SQRT {2} $ imes$ SQRT {2} $ imes$2 }} arrangement. The precipitation reaction of Zn3P2 was explained by an atomic migration model based on the kick-out mechanism.