  We show that the Cherenkov Telescope Array (CTA) can realistically challenge
the Inert Doublet Model, excluding its heavy regime up to dark matter masses of
800 GeV and probing a large fraction of the remaining viable parameter space at
even higher masses. Two features of the Inert Doublet Model make it
particularly suitable for CTA searches. First, the dark matter mass (in the
heavy regime) must be larger than 500 GeV. Second, the dark matter annihilation
cross section, $\sigma v$, is always larger than the thermal one, reaching
values as high as $10^{-25} \mathrm{cm^3s^{-1}}$. This higher value of $\sigma
v$ is the result of the unavoidable coannhilation effects that determine the
relic density via thermal freeze-out in the early Universe. We find that with
100 hours of Galactic Center exposure, CTA's expected limit widely surpasses,
even after the inclusion of systematic errors, current and projected bounds
from Fermi-LAT and HESS on this model.
