String theory on 2-d charged black holes corresponding to SL(2)XU(1)(L)/U1 exact asymmetric quotient CFTs are investigated. These backgrounds can be embedded, in particular, in a two dimensional heterotic string. In the extremal case, the quotient CFT description captures the near horizon physics, and is equivalent to strings in AdS(2) with a gauge field. Such string vacua possess an infinite space-time Virasoro symmetry, and hence enhancement of global space-time Lie symmetries to affine symmetries, in agreement with the conjectured AdS(2)/CFT1 correspondence. We argue that the entropy of these 2-d black holes in string theory is compatible with semi-classical results, and show that in perturbative computations part of an incoming flux is absorbed by the black hole. Moreover, on the way we find evidence that the 2-d heterotic string is closely related to the N = (2, 1) string, and conjecture that they are dual [3].