  The Holstein model is a paradigmatic description of the electron-phonon
interaction, in which electrons couple to local dispersionless phonon modes,
independent of momentum. The model has been shown to host a variety of ordered
ground states such as charge density wave (CDW) order and superconductivity on
several geometries, including the square, honeycomb, and Lieb lattices. In this
work, we study CDW formation in the Holstein model on the kagome lattice, using
a recently developed hybrid Monte Carlo simulation method. We present evidence
for $\sqrt{3} \times \sqrt{3}$ CDW order at an average electron filling of
$\langle n \rangle =2/3$ per site, with an ordering wavevector at the
$K$-points of the Brillouin zone. We estimate a phase transition occurring at
$T_{c}\approx t/18$, where $t$ is the nearest-neighbor hopping parameter. Our
simulations find no signature of CDW order at other electron fillings or
ordering momenta for temperatures $T \geq t/20$.
