We report on the finding of the strongest Hα emission - pseudoequivalent width of 705 Å- known so far in a young, late type dwarf. This object, named as S Ori 71, is a substellar candidate member of the 1-8 Myr star cluster sigma Orionis. Due to its overluminous location in color-magnitude diagrams, S Ori 71 might be younger than other cluster members, or a binary of similar components. Its mass is in the range 0.021-0.012 Msun, depending on evolutionary models and possible binarity. The broad Hα line of S Ori 71 appears asymmetric, indicative of high velocity mass motions in the Hα forming region. The origin of this emission is unclear at the present time. We discuss three possible scenarios: accretion from a disk, mass exchange between the components of a binary system, and emission from a chromosphere. These observations were collected at the VLT of the ESO (Chile), the Keck I telescope (USA), and the 3.5-m telescope at Calar Alto Observatory (Spain).