Formulating consistent theories describing strongly correlated metallic topological phases is an outstanding problem in condensed-matter physics. I will present an explicit construction of a fractionalized analog of the Weyl semimetal state: the fractional chiral metal. Our approach is to construct a 4+1D quantum Hall insulator by stacking 3+1D Weyl semimetals in a magnetic field. In a strong enough field, the low-energy physics is determined by the lowest Landau level of each Weyl semimetal, which is highly degenerate and chiral, motivating us to use a coupled-wire approach. In the presence of electron-electron interactions a gapped phase emerges; its electromagnetic response is given in terms of a Chern-Simons field theory. A boundary of this four dimensional phase remains gapless. The boundary's response to an external electromagnetic field is determined by a chiral anomaly with a fractional coefficient. We suggest that such an anomalous response can be taken as a working definition of a fractionalized strongly correlated analog of the Weyl semimetal state