We report on our continuing effort to identify extremely low-mass members of the cluster around the hot star sigma Orionis. Using the KeckI telescope in Hawaii and the Isaac Newton telescope in La Palma, we carried out a deep near-infrared and optical search in an area of 55 square arcminutes, which has yielded the discovery of an object with blue near-infrared color (J-H=-0.11) and very red optical color (I-J=4.85). Such colors are characteristic of the coolest dwarfs, which have a spectral energy distribution dominated by strong methane and water molecular bands. A near-infrared spectrum obtained with the KeckI telescope confirms the presence of methane bands. Comparison of our Keck spectrum with synthetic spectra, provided by France Allard, yields a temperature in the range 700--1000 K and gravity log g=4.0 +/- 0.5. These physical parameters indicate that the object is associated to the very young star sigma Orionis, and therefore we obtain an age in the range 1-8 Myr, from which we derive a mass between 2 and 7 Jupiter masses. This object, which we have named SOri70, is the lowest mass planet-like object imaged to date, and suggests that planetary mass objects free floating in space can be numerous.