  We argue that a correlated fluid of electrons and holes can exhibit a
fractional quantum Hall effect at zero magnetic field analogous to the Laughlin
state at filling $1/m$. We introduce a variant of the Laughlin wavefunction for
electrons and holes and show that for $m=1$ it is the exact ground state of a
free fermion model that describes $p_x + i p_y$ excitonic pairing. For $m>1$ we
develop a simple composite fermion mean field theory, and we present evidence
that our wavefunction correctly describes this phase. We derive an interacting
Hamiltonian for which our wavefunction is the exact ground state, and we
present physical arguments that the $m=3$ state can be realized in a system in
which energy bands with angular momentum that differ by $3$ cross at the Fermi
energy. This leads to a gapless state with $(p_x + i p_y)^3$ excitonic pairing,
which we argue is conducive to forming the fractional excitonic insulator in
the presence of interactions. Prospects for numerics on model systems and band
structure engineering to realize this phase in real materials are discussed.
