Possible Anti-Pfaffian Pairing of Composite Fermions in the Lowest Landau Level

We predict that an incompressible fractional quantum Hall state is likely to form at $\nu =3\mathrm{/}8$ as a result of a chiral p-wave pairing of fully spin polarized composite fermions carrying four quantized vortices, and that the pairing is of the Anti-Pfaffian kind. Possible experimental ramifications are discussed.