  Two-dimensional $p_x+ip_y$ topological superconductors host gapless Majorana
edge modes, as well as Majorana bound states at the core of $h/2e$ vortices.
Here we construct a model realizing the fractional counterpart of this phase: a
fractional chiral superconductor. Our model is composed of an array of coupled
Rashba wires in the presence of strong interactions, Zeeman field, and
proximity coupling to an $s$-wave superconductor. We define the filling factor
as $\nu=l_{\text{so}}n/4$, where $n$ is the electronic density and
$l_{\text{so}}$ is the spin-orbit length. Focusing on filling $\nu=1/m$, with
$m$ being an odd integer, we obtain a tractable model which allows us to study
the properties of the bulk and the edge. Using an $\epsilon$-expansion with
$m=2+\epsilon$, we show that the bulk Hamiltonian is gapped and that the edge
of the sample hosts a chiral $\mathbb{Z}_{2m}$ parafermion theory with central
charge $c=\frac{2m-1}{m+1}$. The tunneling density of states associated with
this edge theory exhibits an anomalous energy dependence of the form
$\omega^{m-1}$. Additionally, we show that $\mathbb{Z}_{2m}$ parafermionic
bound states reside at the cores of $h/2e$ vortices. Upon constructing an
appropriate Josephson junction in our system, we find that the current-phase
relation displays a $4\pi m$ periodicity, reflecting the underlying non-abelian
excitations.
