When a liquid is supercooled and begins to crystallize, the stable solid phase grows and penetrates into the metastable liquid phase. The resulting crystallites often appear as finger-like dendrites(1,2) which branch as they grow into complex structures, similar in appearance to the arms of a snowflake(3). The basic pattern of dendritic growth is common to many systems undergoing phase transitions, is observed during viscous fingering and electrochemical deposition, and plays an important role in determining the strength of cast metals(4). Here we report the results of experiments which show that dendritic growth can also occur in the very different context of electrohydrodynamic convection. In a nematic liquid crystal, convective now fan be induced by the application of a sufficiently strong electric field. We find that, at the onset of convection, the convective state can invade the equilibrium state in the form of dendritic patterns. These results, which cannot be explained in terms of the existing theory for electrohydrodynamic convection, imply that the phenomenon of dendritic growth is far more ubiquitous than was previously suspected.