We present here the first study on the stability of plane Poiseuille flow when the fluid is stratified in density perpendicularly to the plane of horizontal shear. Using laboratory experiments, linear stability analyses and direct numerical simulations, we describe the appearance of an instability that results from a resonance of internal gravity waves and Tollmien–Schlichting waves carried by the flow. This instability takes the form of long meanders confined in thin horizontal layers stacked along the vertical axis.