The impact of a chain of thin magnetic islands on the stability of electrostatic drift modes is studied for plasma confined by a sheared slab magnetic field geometry. Small magnetic islands are considered, with a width comparable to the ion Larmor radius. Gyrokinetic theory is employed to derive self-consistently the equilibrium modifications due to the island chain, as well as the drift mode structure and stability. The island has two effects on the equilibrium: it modifies the density and temperature gradients and, in general, strong sheared plasma flows must exist in its vicinity. A reduced model is developed to illustrate the impact of this new equilibrium on drift modes, focusing on the ion temperature gradient (ITG) mode. It is found that magnetic islands tend to stabilize these modes. The ITG mode structure is also studied. In the absence of magnetic islands, the drift modes are plane waves of constant amplitude in the y-direction (magnetic flux surfaces are defined by the x–y plane, with inhomogeneities in the x-direction and the main component of magnetic field in the z-direction). However, the drift modes become more localized in the y-direction in the presence of magnetic islands. An interesting result is that the position of localization is not where the drive for the instability is strongest. An analytic WKB theory is presented for a simplified model which sheds light on this result.