Syndiotactic poly(3-methyl-1-butene) (sP3MB) has been obtained for the first time by hydrogenation of 3,4-dpoly(isoprene), which in turn has been synthesized with the catalyst FeCl2(2,2'-bipyridine)(2) activated with methylaluminoxane. The synthesized sample of sP3MB is amorphous but crystallizes by stretching and annealing of the oriented amorphous phase at 60-70 degrees C. The diffraction image of the annealed fibers shows only three equatorial reflections and a few weak reflections distributed on three nonequatorial layer lines. From these data a model of the conformation of the chains of sP3MB is proposed. The chains of sP3MB assume in the crystalline phase a 3/1 helical conformation, providing the first example of a syndiotactic polymer with 3-fold helical chains. A high degree of disorder is present in the crystals so that the structure can be described by an arrangement of parallel conformationally ordered 3/1 helical chains and disorder in the lateral correlations between the chains.