  The spin-4/3 fractional superstring is characterized by a chiral algebra
involving a spin-4/3 current on the world-sheet in addition to the
energy-momentum tensor. These currents generate physical state conditions on
the fractional superstring Fock space. Scattering amplitudes of these physical
states are described which satisfy both spurious state decoupling and cyclic
symmetry (duality). Examples of such amplitudes are calculated using an
explicit $c=5$ realization of the spin-4/3 current algebra. This representation
has three flat coordinate boson fields and a global SO(2,1) Lorentz symmetry,
permitting a particle interpretation of the amplitudes.
