The fronts of flowing granular media often manifest fingered patterns. For the case of a granular flow down an inclined plane, Pouliquen, Delour and Savage (1997) have proposed that such patterns are induced by the segregation of coarse irregularly shaped particles. Here, we consider a thin layer of a granular medium flowing within a cylinder that is rotated about its horizontal axis of symmetry. Our results show that-even when the medium is well-sieved and consists of nearly spherical grains-its leading edge may develop fingers. This suggests that, in general flow configurations, mechanisms other than segregation by particle type may be active in the instability of a straight front.