  We construct five dimensional black rings in global anti-de Sitter space
using numerical methods. These rings satisfy the BPS bound $| J | < M \ell$,
but the angular velocity always violates the Hawking-Reall bound $| \Omega_H
\ell | \leq 1$, indicating that they should be unstable under superradiance. At
high temperatures, the limit $| \Omega_H \ell | \searrow 1$ is attained by thin
rings with an arbitrarily large radius. However, at sufficiently low
temperatures, this limit is saturated by a new kind of rings, whose outer
circle can still be arbitrarily long while the hole in the middle does not grow
proportionally. This gives rise to a membrane-like horizon geometry, which does
not have an asymptotically flat counterpart. We find no evidence for thin AdS
black rings whose transverse $S^2$ is much larger than the radius of AdS,
$\ell$, and thus these solutions never fall into the hydrodynamic regime of the
dual CFT. Thermodynamically, we find that AdS black rings never dominate the
grand canonical ensemble. The behaviour of our solutions in the microcanonical
ensemble approaches known perturbative results in the thin-ring limit.
