  We investigate the effect of substituting Si for Ge in the ferromagnetic
superconductor UCoGe. Dc-magnetization, ac-susceptibility and electrical
resistivity measurements on polycrystalline UCoGe$_{1-x}$Si$_x$ samples show
that ferromagnetic order and superconductivity are progressively depressed with
increasing Si content and simultaneously vanish at a critical concentration
$x_{cr} \simeq 0.12$. The non-Fermi liquid temperature variation in the
electrical resistivity near $x_{cr}$ and the smooth depression of the ordered
moment point to a continuous ferromagnetic quantum phase transition.
Superconductivity is confined to the ferromagnetic phase, which provides
further evidence for magnetically mediated superconductivity.
