We report on the experimental observation of the instability of a plasma shell, which formed during the expansion of a laser-ablated plasma into a rarefied ambient medium. By means of a proton radiography technique, the evolution of the instability is temporally and spatially resolved on a time-scale much shorter than the hydrodynamic one. The density of the thin shell exceeds that of the surrounding plasma, which lets electrons diffuse outwards. An ambipolar electric field grows on both sides of the thin shell that is antiparallel to the density gradient. Ripples in the thin shell result in a spatially varying balance between the thermal pressure force mediated by this field and the ram pressure force that is exerted on it by the inflowing plasma. This mismatch amplifies the ripples by the same mechanism that drives the hydrodynamic non-linear thin-shell instability (NTSI). Our results thus constitute the first experimental verification that the NTSI can develop in colliding flows.