  We consider a class of 4D supersymmetric black hole solutions, arising from
string theory compactifications, which classically have vanishing horizon area
and singular space-time geometry. String theory motivates the inclusion of
higher derivative terms, which convert these singular classical solutions into
regular black holes with finite horizon area. In particular, the supersymmetric
attractor equations imply that the central charge, which determines the radius
of the $AdS_2\times S^2$ near horizon geometry, acquires a non-vanishing value
due to quantum effects. In this case quantum corrections to the
Bekenstein-Hawking relation between entropy and area are large. This is the
first explicit example where stringy quantum gravity effects replace a
classical null singularity by a black hole with finite horizon area.
