  We construct probe solutions in the attractor background of the
five-dimensional D1-D5-P black hole which represent near-horizon microstates in
the limit of large D1-charge. These generalize the corresponding solutions
considered by Gaiotto, Strominger and Yin for the 4-dimensional D0-D4 black
hole. Using U-duality and a 4D-5D connection, we argue that the relevant
configurations are bound states of D1-branes that have expanded through the
Myers effect to form a Kaluza-Klein monopole wrapping the black hole horizon.
We show that these branes experience a magnetic field on their moduli space,
and that the degeneracy of lowest Landau levels reproduces the
Bekenstein-Hawking entropy.
