  A set of reduced Hall magnetohydrodynamic (MHD) equations are used to
evaluate the stability of large aspect ratio current sheets to the formation of
plasmoids (secondary islands). Reconnection is driven by resistivity in this
analysis, which occurs at the resistive skin depth $d_\eta \equiv S_L^{-1/2}
\sqrt{L v_A/\gamma}$, where $S_L$ is the Lundquist number, $L$ the length of
the current sheet, $v_A$ the Alfv\'{e}n speed, and $\gamma$ the growth rate.
Modifications to a recent resistive MHD analysis [N.\ F.\ Loureiro, A.\ A.\
Schekochihin, and S.\ C. Cowley, Phys.\ Plasmas {\bf 14}, 100703 (2007)] arise
when collisions are sufficiently weak that $d_\eta$ is shorter than the ion
skin depth $d_i \equiv c/\omega_{pi}$. Secondary islands grow faster in this
Hall MHD regime: the maximum growth rate scales as $(d_i/L)^{6/13} S_L^{7/13}
v_A/L$ and the number of plasmoids as $(d_i/L)^{1/13} S_L^{11/26}$, compared to
$S_L^{1/4} v_A/L$ and $S^{3/8}$, respectively, in resistive MHD.
