The semicollisional layer equations governing the linear stability of small mode number tearing modes in a low beta, large aspect ratio, tokamak equilibrium are derived from an expansion of the gyrokinetic equation. In this analysis only the cases where the ion Larmor radius is either much less than, or much greater than, the layer width are considered. Both the electrons and the ions are assumed to lie in the banana collisionality regime. One interesting feature of the derived layer equations, in the limit of small ion Larmor radius, is a substantial reduction in the effective collisionality of the system due to neoclassical ion dynamics. Next, using a shooting code, a dispersion relation is obtained from the layer equations in the limits of small ion Larmor radius and a vanishingly small fraction of trapped particles. As expected, strong semicollisional stabilization of the mode is found, but, in addition, a somewhat weaker destabilizing effect is obtained in the transition region between the collisional and semicollisional regimes.