  We present a model to explain LHCb's recent measurements of $R_K$ and
$R_{K^{\ast}}$ based on an anomaly-free, spontaneously-broken $U(1)_F$ gauge
symmetry, without any fermionic fields beyond those of the Standard Model (SM).
The model explains the hierarchical heaviness of the third family and the
smallness of quark mixing. The $U(1)_F$ charges of the third family of SM
fields and the Higgs doublet are set equal to their respective hypercharges. A
heavy $Z^\prime$ particle with flavour-dependent couplings can modify the
$[\overline{b_L} \gamma^\rho s_L][\overline{\mu_L} \gamma_\rho \mu_L]$
effective vertex in the desired way. The $Z^\prime$ contribution to
$B_s-\overline{B_s}$ mixing is suppressed by a small mixing angle connected to
$V_{ts}$, making the constraint coming from its measurement easier to satisfy.
The model can explain $R_K$ and $R_{K^{(\ast)}}$ whilst simultaneously passing
other constraints, including measurements of the lepton flavour universality of
$Z$ couplings.
