The influence of epitaxial strain on the anti-ferromagnetic ordering was studied in a 450-nm-thick Cr film grown on a MgO(001) substrate by molecular beam epitaxy. The anti-ferromagnetic nature of the films was probed by neutron diffraction. A detailed structural characterization of the film was carried out by atomic force microscopy, Rutherford backscattering/channeling spectrometry, and X-ray diffraction. At low temperatures a transverse spin density wave with propagation vector in the film plane is detected, and is attributed to the presence of epitaxial strain. Crystal defects in the sample lead to the appearance of the commensurate anti-feffomagnetic state at higher temperatures.