  The presence of muons in air-showers initiated by cosmic ray protons and
nuclei is well established as a powerful tool to separate such showers from
those initiated by gamma rays. However, so far this approach has been fully
exploited only for ground level particle detecting arrays. We explore the
feasibility of using Cherenkov light from muons as a background rejection tool
for imaging atmospheric Cherenkov telescope arrays at the highest energies. We
adopt an analytical model of the Cherenkov light from individual muons to allow
rapid simulation of a large number of showers in a hybrid mode. This allows us
to explore the very high background rejection power regime at acceptable cost
in terms of computing time. We show that for very large ($\gtrsim$20 m mirror
diameter) telescopes, efficient identification of muon light can potentially
lead to background rejection levels up to 10$^{-5}$ whilst retaining high
efficiency for gamma rays. While many challenges remain in the effective
exploitation of the muon Cherenkov light in the data analysis for imaging
Cherenkov telescope arrays, our study indicates that for arrays containing at
least one large telescope, this is a very worthwhile endeavor.
