  Despite mounting evidence that dark matter (DM) exists in the Universe, its
fundamental nature remains unknown. We present sensitivity estimates to detect
DM particles with a future very-high-energy ($\gtrsim$ TeV) wide field-of-view
gamma-ray observatory in the Southern Hemisphere. This observatory would search
for gamma rays from the annihilation or decay of DM particles in the Galactic
halo. With a wide field of view, both the Galactic Center and a large fraction
of the Galactic halo will be detectable with unprecedented sensitivity to DM in
the mass range of $\sim$500 GeV to $\sim$2 PeV. These results, combined with
those from other present and future gamma-ray observatories, will likely probe
the thermal relic annihilation cross section of Weakly Interacting Massive
Particles for all masses from $\sim$80 TeV down to the GeV range in most
annihilation channels.
