We report very intense and variable Hα emission (pseudoequivalent widths of ~180 and 410 Å) of S Ori 55, a probable free-floating, M9-type substellar member of the young σ Orionis open star cluster. After comparison with state-of-the-art evolutionary models, we infer that S Ori 55 is near or below the cluster deuterium-burning mass borderline, which separates brown dwarfs and planetary-mass objects. We find its mass to be 0.008-0.015 Msolar for ages between 1 and 8 Myr, with ~0.012 Msolar the most likely value at the cluster age of 3 Myr. The largest Hα intensity reached the saturation level of log(LHα/Lbol)=-3. We discuss several possible scenarios for such a strong emission. We also show that σ Ori M and L dwarfs have, in general, more Hα emission than their older field spectral counterparts. This could be due to a decline in the strength of the magnetic field with age in brown dwarfs and isolated planetary-mass objects or to a likely mass accretion from disks in the very young σ Ori substellar members.