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Single-phase and single-oriented epitaxial Cr2O3 thin film has been grown on SrTiO3 (1 1 1) substrate for the first time. The morphology, epitaxial growth mode and oxygen stoichiometry of the obtained film have been investigated by AFM, XRR, XRD and XPS, and compared to thin film grown on alfa-Al2O3 under equivalent conditions. The Cr2O3/SrTiO3 system presents a non-coincidence growth based on in&#-plane rotation of 30° of the Cr2O3 layer respect to the underlying SrTiO3 (1 1 1) substrate, while a coincidence growth based on axis-on-axis coupling is present for Cr2O3-Al2O3. However, in both cases an in-plane compression occurs in order to match the layer and substrate lattices. The formation of punctual defects in the form of oxygen vacancies have been observed by XPS for the layer grown on alfa-Al2O3, being the main mechanism for strain alleviation (4%). However, the 18 nm thick layer grown on SrTiO3 presents stoichiometric oxygen content maintaining an epitaxial strain (1.6%) accumulated on the lattice. Both epitaxial Cr2O3 layers show soft ferromagnetic response with coercive fields of 60 Oe and 90 Oe for the layer grown on SrTiO3 and alfa-Al2O3, respectively.