It is argued, using an M-theory lift, that the IIA partition function on a
euclidean AdS_2 x S^2 x CY_3 attractor geometry computes the modified elliptic
genus Z_BH of the associated black hole in a large charge expansion. The
partition function is then evaluated using the Green-Schwarz formalism. After
localizing the worldsheet path integral with the addition of an exact term,
contributions arise only from the center of AdS_2 and the north and south poles
of S^2. These are the toplogical and anti-topological string partition
functions Z_top and {\bar Z_top} respectively. We thereby directly reproduce
the perturbative relation Z_BH = |Z_top|^2.