Filamented electron beams have been observed to be emitted from the rear of thin solid targets irradiated by a high-intensity short-pulse laser when there is low-density plasma present at the back of the target. These observations are consistent with a laser-generated beam of relativistic electrons propagating through the target, which is subsequently fragmented by a Weibel-like instability in the low-density plasma at the rear. These measurements are in agreement with particle-in-cell simulations and theory, since the filamentation instability is predicted to be dramatically enhanced when the electron beam density approaches that of the background plasma.