  Thin current sheets in systems of large size that exceed a critical value of
the Lundquist number are unstable to a super-Alfvenic tearing instability. The
scaling of the growth rate of the fastest growing instability with respect to
the Lundquist number is shown to follow from the classical dispersion relation
for tearing modes. As a result of this instability, the system realizes a
nonlinear reconnection rate that appears to be weakly dependent on the
Lundquist number, and larger than the Sweet-Parker rate by an order of
magnitude (for the range of Lundquist numbers considered). This regime of fast
reconnection appears to be realizable in a dynamic and highly unstable thin
current sheet, without requiring the current sheet to be turbulent.
