Possible Anti-Pfaffian Pairing of Composite Fermions at ν=3/8

We predict that an incompressible fractional quantum Hall state is likely to form at nu = 3/8 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. Experimental ramifications include quasiparticles with non-Abelian braid statistics and upstream neutral edge modes.