  TeV-scale particles that couple to the standard model through the weak force
represent a compelling class of dark matter candidates. The search for such
Weakly Interacting Massive Particles (WIMPs) has already spanned multiple
decades, and whilst it has yet to provide any definitive evidence for their
existence, viable parameter space remains. In this paper, we show that the
upcoming Cherenkov Telescope Array (CTA) has significant sensitivity to
uncharted parameter space at the TeV mass scale. To do so, we focus on two
prototypical dark matter candidates, the Wino and Higgsino. Sensitivity
forecasts for both models are performed including the irreducible background
from misidentified cosmic rays, as well as a range of estimates for the
Galactic emissions at TeV energies. For each candidate, we find substantial
expected improvements over existing bounds from current imaging atmospheric
Cherenkov telescopes. In detail, for the Wino we find a sensitivity improvement
of roughly an order of magnitude in $\langle \sigma v \rangle$, whereas for the
Higgsino we demonstrate that CTA has the potential to become the first
experiment that has sensitivity to the thermal candidate. Taken together, these
enhanced sensitivities demonstrates the discovery potential for dark matter at
CTA in the 1-100 TeV mass range.
