  The accurate determination of the elemental composition of cosmic rays at
high energies is expected to provide crucial clues on the origin of these
particles. Previous direct measurements of composition have been limited by
experiment collecting power, resulting in marginal statistics above $10^{14}$
eV, precisely the region where the ``knee'' of the cosmic-ray energy spectrum
is starting to develop. In contrast, indirect measurements using extensive air
showers can produce sufficient statistics in this region but generate elemental
measurements which have relatively large uncertainties. Here we discuss a
technique which has become possible through the use of modern ground-based
Cerenkov imaging detectors. We combine a measurement of the Cerenkov light
produced by the incoming cosmic-ray nucleus in the upper atmosphere with an
estimate of the total nucleus energy produced by the extensive air shower
initiated when the particle interacts deeper in the atmosphere. The emission
regions prior to and after the first hadronic interaction can be separated by
an imaging Cerenkov system with sufficient angular and temporal resolution.
Monte Carlo simulations indicate an expected charge resolution of $\Delta Z/Z
<5%$ for incident iron nuclei in the region of the ``knee'' of the cosmic-ray
energy spectrum. This technique also has the intriguing possibility to
unambiguously discover nuclei heavier than iron at energies above 10$^{14}$ eV.
The identification and rejection of background produced by charged particles in
ground based gamma-ray telescopes is also discussed.
