  We suggest a construction of a large class of topological states using an
array of quantum wires. First, we show how to construct a Chern insulator using
an array of alternating wires that contain electrons and holes, correlated with
an alternating magnetic field. This is supported by semi-classical arguments
and a full quantum mechanical treatment of an analogous tight-binding model. We
then show how electron-electron interactions can stabilize fractional Chern
insulators (Abelian and non-Abelian). In particular, we construct a relatively
stable non-Abelian $\mathbb{Z}_{3}$ parafermion state. Our construction is
generalized to wires with alternating spin-orbit couplings, which give rise to
integer and fractional (Abelian and non-Abelian) topological insulators. The
states we construct are effectively two-dimensional, and are therefore less
sensitive to disorder than one-dimensional systems. The possibility of
experimental realization of our construction is addressed.
