  Cobalt disilicide provides a promising nearly-epitaxial superconducting
material on silicon, which is compatible with high-density integrated circuit
technology. We have characterized CoSi$_{2}$ superconducting microwave cavities
around 5.5 GHz for resonance frequency fluctuations at temperatures 10 - 200
mK. We found relatively weak fluctuations $(\delta f/f)^2$ following the
spectral density $A/f^{\gamma} $, with $A \simeq 6 \times 10^{-16}$ and
$\gamma$ slightly below 1 at an average number of photons of $10^4$; the noise
decreased with measurement power as $1/P^{1/2}$. We identify the noise as
arising from kinetic inductance fluctuations and discuss possible origins of
such fluctuations.
