We report on the discovery of a free-floating methane dwarf toward the direction of the young star cluster σ Ori. Based on the object's far-red, optical, and near-infrared photometry and spectroscopy, we conclude that it is a possible member of this association. We have named it S Ori J053810.1-023626 (S Ori 70 is the abridged name). If it is a true member of σ Ori, the comparison of the photometric and spectroscopic properties of S Ori 70 with state-of-the-art evolutionary models yields a mass of 3+5-1 Jupiter mass for ages between 1 and 8 Myr. The presence of such a low-mass object in our small search area (55.4 arcmin2) would indicate a rising substellar initial mass function in the σ Ori cluster, even for planetary masses.