An electron thermal instability is proposed, which could explain the occurrence of the break-up of a plasma shell into separated current elements during the early history of a discharge. Inclusion of electron thermal conduction and Faraday's law leads to an optimum wavelength for growth, in good agreement with recent results on a θ pinch at NRL, Washington. Finally, the addition of ion motion leads to a modification of the stability criterion. The non-convective instability exists only at low temperature and high density; but a convective instability now appears, which persists at high temperature, and could be relevant to fusion conditions.