The weakly nonlinear amplitude growth of slightly oblique instability waves in an incompressible free shear layer is shown to be first influenced by three-dimensionality in a limiting case for large Reynolds number when a particular order relationship is chosen between the spanwise scale and the amplitude of the small disturbance. The formulation resembles that for purely two-dimensional motion but includes the effect of vortex stretching in the nonequilibrium, nonlinear, viscous critical layer.