  Non-ionized media subject to strong fields can become locally ionized by
penetration of finger-shaped streamers. We study negative streamers between
planar electrodes in a simple deterministic continuum approximation. We observe
that for sufficiently large fields, the streamer tip can split. This happens
close to Firsov's limit of `ideal conductivity'. Qualitatively the tip
splitting is due to a Laplacian instability quite like in viscous fingering.
For future quantitative analytical progress, our stability analysis of planar
fronts identifies the screening length as a regularization mechanism.
