Clathrate materials have been the subject of intense interest and research for thermoelectric application. Nevertheless, from the very large number of conceivable clathrate structures, only a small fraction of them have been examined. Since the thermal conductivity of clathrates is inherently small due to their large unit cell size and open-framework structure, the current research on clathrates is focused on finding the ones with large thermoelectric power factor. Here we predict an extraordinarily large power factor for type-VIII clathrate Si(46). We show the existence of a large density of closely packed elongated ellipsoidal carrier pockets near the band edges of this so far hypothetical material structure, which is higher than that of the best thermoelectric materials known today. The high crystallographic symmetry near the energy band edges for Si(46)-VIII clathrates is responsible for the formation of such a large number of carrier pockets.