We observed experimentally a new regime for granular flows in an inclined channel with a flow-rate-controlled system. For high flow rates, the flow occurs atop a static granular heap whose angle is considerably higher than those usually exhibited by granular heaps. The properties of such superstable heaps (SSH) are drastically affected by a change in the channel width W. This indicates that the unusual stability of these heaps can be accounted for by the flowing layer and its friction on the sidewalls. A simple depth-averaged model, assuming Coulomb friction, shows that the SSH angle scales as h/W (W being the channel width), and that grain size plays no part.