We investigate the structure of the conduction minibands in a two‐dimensional periodic array of rectangular quantum wires. The finite barrier height in such a GaAs/Ga1−xAlxAs heterostructure gives rise to a ‘‘checker‐board’’ pattern of wells and barriers, i.e., a checker‐board superlattice (CBSL). The energy bands are obtained using the finite element method, in the effective mass approximation, with current continuity at interfaces. The free‐carrier‐induced optical nonlinear susceptibility χ(3) due to band nonparabolicity in the CBSL is obtained in both the rectangular directions. Our calculations predict an increase in χ(3) of about 1–2 orders of magnitude over bulk GaAs, for specific ranges of carrier concentrations.