Black hole bound states in AdS(3) x S**2

We systematically construct the geometries dual to the 1+1 dimensional (0,4) conformal field theories that arise in the low-energy description of wrapped M5-branes in S^1 x CY_3 compactifications of M-theory. This includes a large number of multicentered black hole bound states asymptotic to AdS_3 x S^2. In addition, we find many geometries that develop multiple, mutually decoupled AdS_3 x S^2 throats. We argue there is a useful one to one correspondence between the connected components of the space of solutions and particular limits of type IIA attractor flow trees. We point out that there is a thermodynamic instability of small supersymmetric BTZ black holes to localization on the S^2, a supersymmetric and exactly solvable analog of the well known AdS-Schwarzschild localization instability, and identify this with the "Entropy Enigma" in four dimensions. We discuss the phase transition this suggests, and initiate the CFT interpretation of these results.