Insulating Z2 spin liquids are a phase of matter with bulk anyonic quasiparticle excitations and ground-state degeneracies on manifolds with nontrivial topology. We construct a time-reversal symmetric Z2 spin liquid in two spatial dimensions using an array of quantum wires. We identify the anyons as kinks in the appropriate Luttinger-liquid description, compute their mutual statistics, and construct local operators that transport these quasiparticles. We also present a construction of a fractionalized Fermi liquid (FL∗) by coupling the spin sector of the Z2 spin liquid to a Fermi liquid via a Kondo-like coupling. © 2016 American Physical Society.